@blackpenredpen now solve Integral {[(e power sinx + sqrt(cosx+tanx)] power pi} ---------------------------------------- [ln (ln (cosec x)) + sqrt(sec²x+cot²x)]
@@pitoachumi2663 bro u r so right. I just started calculus and it is already hard. But the truth is this one was extremeley satisfying. But the truth is that in India the most difficult questions would be very easily solved by the teachers but we end up gettting dumbfounded by the same questions. It's annoying but fun.
If you love physics solve The speed of a motor engine decreases from 900 rev/min. to 600rev / min in in 10 seconds. Calculate: The angular acceleration Number of revolutions made by the motor during this interval How many additional seconds are required for motor to come to rest in the same rate
If you love physics solve find the value of ratio of specific heat capacity for the mixture of gas containing one mole of nitrogen and 2 mole of argon if Gamma of nitrogen is equal to 1.40 and gamma of argon is equal to 1.54
If you love physics solve 3 moles of an ideal gas undergoes a reversible isothermal compression at 27 degree Celsius during this compression 1850 joule of work is done on the gas what is the change in entropy
Time to try it out! sin²+cos²+tan²=1+tan²=sec² (1-2ln(cos))^π ln(csc)+ln(sec)+ln(cot) = -ln(sin)-ln(cos)+ln(cos)-ln(sin) = -ln(sin) d/dx(-2ln(sin)) = -2 × cos/sin = -2cot So the integral becomes sin×(1-2ln(cos))^π / -2cos u = -ln(cos) du = sin/cos dx So (2u+1)^π du Where u = -ln(cos x) Now another substitution w = 2u+1 dw = 2du So -¼×w^π dw Integrates to w^π+1 / (-4)(π+1) w = 2u+1 u = -ln(cos x) w = 1-2ln(cos x) (1-2ln(cos x))^(π+1) / -4(π+1) + C
5:12 My favorite scene because we all know what he means 😂 This problem was actually quite easy for looking so difficult. The only things I didn't instantly see is the u-sub, because I didn't instantly know the derivative of sec(x) Great video!
I love how real the problem creation is. Start with a random smattering of operations and functions that look scary then adjust it until a solvable problem appears.
as a 50 year old I recently(2020-2022) went back and got my associates degrees after a debilitating health incident that left me reconstructing my base of knowledge. I also wanted to work my brain and ended up taking physics and calculus 1 and 2. At the community college level. I still have memory issues but these videos keep me atleast familiar with the concept of integration. I did well almost coming out with an A but for fractions of points in both.. graduated with a 3.92 gpa. the final Bs in calc I and II got my 4.0.. I can now help my highschool and middleschool children when they get stumped in their advanced math classes. I love the depth to which you dive in explaining your process and the sloutions..Your humor is also not lost on me. Fun makes learning more bearable in difficult situations. I only wish my professor was so concerned with teaching the process. After the few example in the book, she assigned out homework. She wanted it the way she taught it but left us to "figure it out" no pun intended.. I would have drowned but for math is power, professor leanard and some of the others. I realized the value of not only knowing but proving the trig identites alittle too late but now I know. I may go back and finish the bachelors in meterology but am leaning toward mathematics just for fun. Keep up the good work, you are opening doors in the minds of many who were traumatized by higher maths as evidenced by the comments.. my only question is whether all the variations of blackpenredpen is actually you? there are several, its hard to tell these days.
True, I love when they teach you the absolute basics and then immediately give you a classwork on the toughest parts without the chance to even study 😀
I’m a high school student rn and I’ve been watching blackpenredpen for a few years now. Well I’ve finally made it to calculus in school and this is the first time in my life I’ve actually understood what happened in the vid (normally id just watch and be interested), pretty cool!
It's like one of those jokes where you can tell he started with the punchline and worked his way back... Problem for students is that if you're stressed out and forget just one of those trig relationships, you're screwed. 😛
You only need one, sin2+cos2=1 and it can be derived from geometry on the fly. Did that more than once in high school. Trig functions are much easier than some integration tricks and substitutions (the hardest part in this solution frankly)
As a grade 12 student myself, I didn't find this too hard. Kinda proud of myself that I am able to do such calculus probelms, with mich ease. Loved the vid.
@@RJiiFin Say whatever you want man, I don't care. I solved the question and I'm proud of it, and no, I don't find it weird to flex about it as a grade 12 student.
The function becomes undefined every (npi/2, n2pi), and the limit of that function as it goes to kpi+(2pi - pi/2) (where k is an element of odd natural numbers) goes to negative infinity and finding the area from a to b of fx under the curve and a , b are discontinous (like they belong to different sections of graph and are being separated by a discontinuity) will always be -inf so to get a determinate area a,b has to be continous
This is the kind of stuff that you throw into Wolfram Alpha when the teachers no longer care about the exact solution steps for integrals. That was a really pleasant discovery for me when I started the math courses after calculus, when the teachers started being like "just find the numerical solution in some way".
We completed indefinite integration in our highschool yesterday and first thing in my mind was to visit bprp... And I did solve it on my own before watching his solution. Yay!
They're actually super simple! If you're trying to find the derivative of x^2+y^3+z^4 Partial derivative of x -- simply treat Y and Z as constants, so you get 2x. That's it!
It's not easy. They're very abstract, so methods work for them even less than for regular ODEs. I guess one trick is assuming separability, and seeing what transpires. So you have a function f(x,y,z). Maybe you're solving something like f_xx=f_yz. Something that looks separable. Just assume f(x,y,z)=X(x)Y(y)Z(z) and see if you can derive a set of solutions.
It's interesting how some integrals on paper look very complicated but you only need calculus 1/AP Calculus AB skills to solve the entire integral, albeit with a lot of steps.
That was so freaking cool. The best part is that even though it's so complicated, a high schooler should be able to do that if they have taken precalculus and calculus!
I can't believe you can solve it just using high school calculus. Now I feel bad for not trying to solve it myself before and not get scared unncessarily.
I followed about 80% of what happened here, as my brain slowly melted over the amount of theory he just casually used towards the end of the explonation.
You are very much like the gentleman that taught me calc 2. Hardest teacher on campus, very well known fact. That said, now that the class is over, i wouldnt have rather taken the class with anyone else. On RateMyProfessor, its very clear if the teacher is rated low because hes a bad teacher, and if hes a tough teacher. I learned that day dont ever let rmp sway you away from a great teacher. Some kids complain too much, and thats all there is to it.
when i was 30 seconds through the video, i saw that there were like 7 minutes of video left i was worried that he would continue to build a monstrosity for another 7 whole minutes
Learn more calculus on Brilliant: 👉brilliant.org/blackpenredpen/ (now with a 30-day free trial plus 20% off with this link!)
Thank you for this information but I really want you to tell some basic for integration thanks you
Thanks from Brazil!!!
🙏♾🎁👏🏻👏🏻👏🏻🎉🎊
@blackpenredpen now solve
Integral
{[(e power sinx + sqrt(cosx+tanx)] power pi}
----------------------------------------
[ln (ln (cosec x)) + sqrt(sec²x+cot²x)]
Nice what is your country name
India
i did not expect such a clean solution for this integral
It was way too easy question though
@@GokuDragon-d4rayyy same pfp
@@canyoupoopwot da fok
@@canyoupoop YO LUFFY wyd learning calc bro😭😭😭
thats the beauty of math!
As a high school cal student, this is, so far, the most satisfying integral I've ever witnessed.
really?
come to india baby ull find satisfying triggers everyday then
@@pitoachumi2663 oooo
@@pitoachumi2663or just use the internet
You better work in your tech support @@pitoachumi2663
@@pitoachumi2663 bro u r so right. I just started calculus and it is already hard. But the truth is this one was extremeley satisfying. But the truth is that in India the most difficult questions would be very easily solved by the teachers but we end up gettting dumbfounded by the same questions. It's annoying but fun.
What the student really needs to learn here is not Calculus, but to control their own panic.
Exactly! It is natural to feel intimidated and want to reach for the biggest weapon, but this beast can be taken down barehanded.
Biggest thing I realized in calculus is it's not that bad if you master trigonometry
Exactly! Like at home sure i have all the time but at the exam I'd feel the cold sweat dripping down my face fr 💀
It’s always so funny to me when you add the sin(x)^2 + cos(x)^2 just to make it look harder but it’s just 1 😂 I love it lol
If you love physics solve
The speed of a motor engine decreases from 900 rev/min. to 600rev / min in in 10 seconds. Calculate:
The angular acceleration
Number of revolutions made by the motor during this interval
How many additional seconds are required for motor to come to rest in the same rate
If you love physics solve
find the value of ratio of specific heat capacity for the mixture of gas containing one mole of nitrogen and 2 mole of argon if Gamma of nitrogen is equal to 1.40 and gamma of argon is equal to 1.54
If you love physics solve
3 moles of an ideal gas undergoes a reversible isothermal compression at 27 degree Celsius during this compression 1850 joule of work is done on the gas what is the change in entropy
@@DiverseDose11i was literally revising this exact topic ill solve it when i finish revising
@@NiceLol-dl6lq yeah it will be nice 👍
“Everybody’s here”
I love that part.
smash bros but it’s an integral
What a glorious result! I'm going to make this extra credit the first time I teach a calculus class!
😆
Epik
All your students who watch blackpenredpen: STONKS!
@@caroot1085 If they watch this, they deserve the score
This is the only guy that can make math fun. Keep up the amazing content!
Thanks!!
Time to try it out!
sin²+cos²+tan²=1+tan²=sec²
(1-2ln(cos))^π
ln(csc)+ln(sec)+ln(cot)
= -ln(sin)-ln(cos)+ln(cos)-ln(sin)
= -ln(sin)
d/dx(-2ln(sin)) = -2 × cos/sin
= -2cot
So the integral becomes
sin×(1-2ln(cos))^π / -2cos
u = -ln(cos)
du = sin/cos dx
So
(2u+1)^π du
Where u = -ln(cos x)
Now another substitution
w = 2u+1
dw = 2du
So -¼×w^π dw
Integrates to
w^π+1 / (-4)(π+1)
w = 2u+1
u = -ln(cos x)
w = 1-2ln(cos x)
(1-2ln(cos x))^(π+1) / -4(π+1) + C
Lmao it has the translate to english button
@@R8Spike and I got Hindi button &
sine = sin (pronounced seen) lol
why didn't you take the w as 1-2ln(cosx) from the beginning it's easier than two substitutions
@@mandarbamane4268 for me it was sine = syn
@@TRT_MOOSIC for me it translated sin to "paaap"
5:12 My favorite scene because we all know what he means 😂
This problem was actually quite easy for looking so difficult. The only things I didn't instantly see is the u-sub, because I didn't instantly know the derivative of sec(x)
Great video!
Stuff like that is why I keep watching this guy
idk what he means
What does he mean
I love how real the problem creation is. Start with a random smattering of operations and functions that look scary then adjust it until a solvable problem appears.
When i saw this, it sort of look solvable and now i see this being solved makes it so satisfying
6:18 Not done the +c 😂😂😂
as a 50 year old I recently(2020-2022) went back and got my associates degrees after a debilitating health incident that left me reconstructing my base of knowledge. I also wanted to work my brain and ended up taking physics and calculus 1 and 2. At the community college level. I still have memory issues but these videos keep me atleast familiar with the concept of integration. I did well almost coming out with an A but for fractions of points in both.. graduated with a 3.92 gpa. the final Bs in calc I and II got my 4.0.. I can now help my highschool and middleschool children when they get stumped in their advanced math classes.
I love the depth to which you dive in explaining your process and the sloutions..Your humor is also not lost on me. Fun makes learning more bearable in difficult situations. I only wish my professor was so concerned with teaching the process. After the few example in the book, she assigned out homework. She wanted it the way she taught it but left us to "figure it out" no pun intended.. I would have drowned but for math is power, professor leanard and some of the others. I realized the value of not only knowing but proving the trig identites alittle too late but now I know. I may go back and finish the bachelors in meterology but am leaning toward mathematics just for fun. Keep up the good work, you are opening doors in the minds of many who were traumatized by higher maths as evidenced by the comments.. my only question is whether all the variations of blackpenredpen is actually you? there are several, its hard to tell these days.
It’s always good when teacher give you things in a test you’ve never seen before, like cscx, secx and cotx
True, I love when they teach you the absolute basics and then immediately give you a classwork on the toughest parts without the chance to even study 😀
I'm in high school and this year we finally did the indefinite integrals. Now I can comprehend some of this man’s videos. Nice solution
The fact that I had to play this video at 2x just gives away how easy that question actually was
As a student that has no idea what half of those term means, it was enjoyable. I’ll take a look at this again once I learned those terms.
it feels so blessed to understand this after taking calc bc
You are so calm, smart and good natured I can't help but smile as I watch you solve these. Good work!
I have not got the faintest idea what he just said, but the way he explained everything made me feel like I did
5:46 I thought he is going to say "pi is just 3"
I'm just impressed he managed to fit it all on the whiteboard.
Your alway best. It seems to be very hard but after your explanation it looks like very easy one. Keep rocking on mathematicians
Thanks a lot 😊
This integral looks so daunting to complete, and watching it quickly simplify down is just really satisfying
I’m a high school student rn and I’ve been watching blackpenredpen for a few years now. Well I’ve finally made it to calculus in school and this is the first time in my life I’ve actually understood what happened in the vid (normally id just watch and be interested), pretty cool!
As a 8th grader I understand absolutely nothing but I like the way he is teaching
do you not do calc in year 8 in america?
@@user-oq7cx2rb4t I am not in America, in our country we learn calculus in grade 12 and college
Bro where do you live that you are doing Calc in year 8?
Instantly assuming he's from the us@@user-oq7cx2rb4t
@@_.Max.i.mus._year 8 is like 14 right? Too old for calc 1. Im my country we have math phd by age 16
That was just beautiful. I've never seen such a complicated integral become so easy in such a low amount of time.
what am i doing here? im a biology major
Understanding the beauty of integration
It's like one of those jokes where you can tell he started with the punchline and worked his way back...
Problem for students is that if you're stressed out and forget just one of those trig relationships, you're screwed. 😛
You only need one, sin2+cos2=1 and it can be derived from geometry on the fly. Did that more than once in high school. Trig functions are much easier than some integration tricks and substitutions (the hardest part in this solution frankly)
I guess that's a problem for the student and a reason to git gud foe the teacher...
@@avelkm doesnt require geometry, just devide by cos^2 or sin^2
@@avelkm to be fair you won't have the time to start deriving some relationships on the fly during a test.
He’s high on pot-nuse
This is one of the most beautiful integrals I've ever seen...
As a grade 12 student myself, I didn't find this too hard. Kinda proud of myself that I am able to do such calculus probelms, with mich ease. Loved the vid.
Well as a grade 11 student myself, I also didn't find this too hard. Kinda weird to flex about that as a grade 12 student though?
@@RJiiFin Say whatever you want man, I don't care. I solved the question and I'm proud of it, and no, I don't find it weird to flex about it as a grade 12 student.
@@RedditChronicles022You obviously do care because you responded 😁
@@RJiiFin Ok well, that's fair. Have a good day tho.
@@RedditChronicles022Thanks, you too! 🙂
I just know basic trigonometry and nothing about calculus but it was satisfying
suprisingly ..it was quite easy for me..i hit it right in the first time...nd....glad to see the answer matched ..as a beginner of integration.
I love how there are black and red whiteboard pen boxes in bulk under his table 🥰
The function becomes undefined every (npi/2, n2pi), and the limit of that function as it goes to kpi+(2pi - pi/2) (where k is an element of odd natural numbers) goes to negative infinity and finding the area from a to b of fx under the curve and a , b are discontinous (like they belong to different sections of graph and are being separated by a discontinuity) will always be -inf so to get a determinate area a,b has to be continous
Now do one with all of the trig functions including the inverse and hyperbolic trig functions.
Ohh so just add random letters until it’s solved! Just amazing 😭😭😭
Pretty much 😆
Best math teacher. You are incredible
This video is great for revising calculus rather than just fun purposes.
This is the kind of stuff that you throw into Wolfram Alpha when the teachers no longer care about the exact solution steps for integrals.
That was a really pleasant discovery for me when I started the math courses after calculus, when the teachers started being like "just find the numerical solution in some way".
NO way how did it fit so perfectly
🗣️ : "This joke is frankly getting kind of stale"
Me : "WHAT?!?!" *STONE COLD INTENSIFIES*
This was a fun one to do! Cool how all the identities and the u-sub lines up nicely
We completed indefinite integration in our highschool yesterday and first thing in my mind was to visit bprp... And I did solve it on my own before watching his solution. Yay!
It turned out really easy
Actually, not everybody is here... You forgot hacoversine and covercosine, for example. Those ones always get left out for some reason.
You could also include the arctrigonometric functions, the hyperbolic and arhyperbolic functions, even arg or atan2 could come into play.
maths is all about approach
everybody can learn fromulae and concepts but approach comes with practice and skills.
I love it how brother gets all gitty to do this problem and then starts cranking 90s with the dry-erase marker.
This only works if you are in the first quadrant. Otherwise, you need to be careful about pulling the 2’s out of natural log.
but in the original integrand, we have in the denominator ln(csc(x)) ln(sec(x)) etc
which means it's restricted to first quadrant by nature
Watching this a month later, where I learnt a bit of diff and int calc, feels so nice to me bc I now understand what these are.
This is possibly the greatest integral I've ever seen!
"a_generic_nerd" needs to be asked "STATE'S RIGHTS TO DO WHAT?"
You're telling me a guy with a confederate flag profile pic couldn't do math? I'm shocked, nay, flabbergasted by this information.
This came out on my birthday and I didnt even notice it 😂
Don’t forget the plus c!
I love how the integral symbol goes slowly losing its power and shrinking more and more lol
Now I know what kind of extra task gonna be solved by my students during their exam tests😁😁😁
I am good teacher, I am good😝
Great video!
The trick here was to keep the sin in the denominator and the sec in the numerator by playing with the negative exponent
I don't understand any of these but I still watch ur vids
Extra Credit: Make lower limit zero and solve for upper limit that makes the definite integral equal to 1.
Can you do content on partial differential equations (PDEs)
They're actually super simple! If you're trying to find the derivative of x^2+y^3+z^4
Partial derivative of x -- simply treat Y and Z as constants, so you get 2x. That's it!
@@mattreichmann8118 that's not what a pde is
It's not easy. They're very abstract, so methods work for them even less than for regular ODEs.
I guess one trick is assuming separability, and seeing what transpires.
So you have a function f(x,y,z). Maybe you're solving something like f_xx=f_yz. Something that looks separable. Just assume f(x,y,z)=X(x)Y(y)Z(z) and see if you can derive a set of solutions.
It's interesting how some integrals on paper look very complicated but you only need calculus 1/AP Calculus AB skills to solve the entire integral, albeit with a lot of steps.
I don't know I of integration but it's always fun to watch people solving it 😅
I love these videos but I have absolutely no idea whether there's a system behind the pen colours or if it's just a semi-random choice thing.
It’s systematic. The red is for important parts, new parts or side notes.
"Can we solve this? - Yes, because I made this!" 😂
That was so freaking cool. The best part is that even though it's so complicated, a high schooler should be able to do that if they have taken precalculus and calculus!
*With enough patience
Wait a second... That's just a voiceless post alveolar fricative!
Why not add some hyperbolic trig while you at it
my ass not understanding what the fuck he just wrote at the start: 👍
I would have forgotten the "+ C", as I always do.
that double tap of pen made me scared, but i mustered courage to face it
Sir I have done this one by myself only and then I checked that mine was correct
Very happy to know that😊
It's astonishing that taking calculus can allow me to understand this even a little bit
I got everything! nice job
Hyperbolic trig next?
This was a very interesting one to solve
Loved it! :D
I like your weird words magic man
funny*
wow its so much easier than i thought
Now add in the hyperbolic and inverse trig functions 🙃
beautifully explained
I'm a 12th CBSE Indian student and trust me we know enough integration to solve this...
channeling my best Thornton Mellon: '4' is the answer...
I can't believe you can solve it just using high school calculus. Now I feel bad for not trying to solve it myself before and not get scared unncessarily.
Nicely solved!
As an 11th grader I understand only parts with cos^2 + sin^2 = 1 and Sin/cos = Tan, cool video
This was a beautiful integral
You forgot hyperbolic sine
love this one, thank you
This looks so hard but is so satisfying
well that was actually pretty easy its just observation and manipulation, got it under a min
“And we’re done‼️😝Look 👀 +C🤪🙈yay☺️😇”
I followed about 80% of what happened here, as my brain slowly melted over the amount of theory he just casually used towards the end of the explonation.
That was clean, i did everything fine except the u sub
Those expression after taking the substitution 😂♥️
You are very much like the gentleman that taught me calc 2. Hardest teacher on campus, very well known fact. That said, now that the class is over, i wouldnt have rather taken the class with anyone else. On RateMyProfessor, its very clear if the teacher is rated low because hes a bad teacher, and if hes a tough teacher. I learned that day dont ever let rmp sway you away from a great teacher. Some kids complain too much, and thats all there is to it.
I love that sin²x+cos²x+tan²x made it easier lol
when i was 30 seconds through the video, i saw that there were like 7 minutes of video left
i was worried that he would continue to build a monstrosity for another 7 whole minutes
This was beautiful
beautiful problem
Bro storing those markers like cash in a bank vault