that's because you're focusing on how the teacher solves a problem and not focusing on the formula. When you familiarize the formula, all you have to do is substitute variables and simplify it with basic algebra. The biggest problem is if you take a calculus course without mastery in algebra.
@@damontayy1272 Calculus has so many formulas, memorizing them isn’t gonna help, you need to physically imbed the fundamental concepts into your mind to familiarize the other concepts
@@jorgegarza4172 I know. But guess what, you have to do hard shit to be able to amount to something. Your professor won't change the syllabus, you have to comply or shift to culinary school.
That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel. This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. @@jorgegarza4172
That's a shortcut for u-sub that only works in special cases. So when you use that shortcut, you _are_ using u-sub. Just like how the method of evaluating rational limits at infinity is just a shortcut for L'Hopital's Rule that only works for certain types of rational/radical functions. But yes, you're right, you don't explicitly have to do the working for it, but this channel was made for beginners.
Exactly, That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel. This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. No more unnecessary steps as part of a long and tedius process.
you don't even need to use substitution for such a simple problem like this, just know that for (x+a)^n, with a being a constant and n being a whole number(negative or positive integer, both work), by integrating you always get [(x+a)^n+1]/(n+1), it's just a simple derivative
Correct. [(ax + b)⁽ⁿ ⁺ ¹⁾]′ = a(n + 1)(ax + b)ⁿ How would you answer the next question: ● Find the primitive function F(x) (i.e. F(x)= ∫f(x)dx) of f(x) = (ax + b)ⁿ (‼️whithout using the standard list of primitive functions.‼️) where x is in the Domain D ⊆ ℝ of f and n ∈ ℤ.
That is just because of the use of a U-Sub implicitly, this shows out the steps for that formula. Don’t remember a formula blindly without understanding it’s derivation
If this channel existed when I was preparing for my calculus exams 20 years ago, I think I would have gotten much better grades!... But TH-cam ITSELF wasn't launched until 2005, so TH-cam didn't exist at all when I was in university. Thanks for making me feel old. 😜 No, but seriously, thanks for these videos! You must be helping the next generation.
Okay so this helped me A LOT. Coming back to school (2 yrs) after being sent across seas and been thrown into a calc 2 class… I remember some things but the really helped me out!!
Using the second fundamental theorem of calculus is clearer , just find the derivative of (x+2) , which is 1 , then mould it properly. Then you get the answer
Not a speedrun at all. Just notice the derivative of that is 1, then treat (x + 2) as if it was what you’re integrating, and (1/3)(x + 2)^3. Should take you 1 or 2 seconds to solve
Oh I just develop the square of the binomial and integrate every term, but your metod it's Very good, if it is something basic, it should be noted that I am just learning to derive/integrate, so I don't know a lot of
You didn't need the du/dx, you could directly go ahead and substitute the u for x+2 and still get the same answer at the end. You made it way more complicated than it qctually is dude.
People will hate on me for this but i do not care. I never liked U sub and never will. I understand the concept and instead just solve the integral using the tabular table instead.
Just use reverse chain rule, and you find out that you divide by 1 (because of the coefficient of x), so you simply have to use the reverse power rule.
we still can't solve the integral of some basic mathematical functions For example, although we can calculate the result of the integral e^sin(x) dx numerically, we cannot express it symbolically. Mathematics is not a science, it is a language. #math #mathematics #integral #sinus #cosinus
In normal way, by expanding (x+2) ^2 and integrating we get : ((x^3) +(12x) +(6(x^2))) /3 But through substitution method : ((x^3) +8+12x+(6(x^2)) ) /3 An additional 8 is coming!!!!!! Iam so confused. Can anyone explain plz 😢!!
This is because you were taught one way as you teach only one way. As if it were the only way. Sadly it's the only way you know and you provide so little worth to your students while you mimmic parrot as a career. Hero to no one.
@@vaishalikarande3246 don't worry, you will learnt all these and more in 2-4 years. Remember the derivative and integrals by heart. It is essential in Univeruty regardless which stream you choose.
reverse chain rule is just the consequence of a u-sub that always works: if ∫ f(x) dx = F(x), then: ∫ f(ax+b) dx {u=ax+b, du= a*dx, dx=du/a} = ∫ f(u) (du/a) = (1/a) ∫ f(u) du = F(u)/a = F(ax+b)/a see
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Calculus is like a Minecraft tutorial it starts off nice, and then the problem immediately starts using 335.67 different letters
Exactly, I was like,
Ok,
Ok, yeah that makes sense
...
WHAT THE F***
that's because you're focusing on how the teacher solves a problem and not focusing on the formula. When you familiarize the formula, all you have to do is substitute variables and simplify it with basic algebra.
The biggest problem is if you take a calculus course without mastery in algebra.
@@damontayy1272 Calculus has so many formulas, memorizing them isn’t gonna help, you need to physically imbed the fundamental concepts into your mind to familiarize the other concepts
@@jorgegarza4172 I know. But guess what, you have to do hard shit to be able to amount to something. Your professor won't change the syllabus, you have to comply or shift to culinary school.
That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel.
This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. @@jorgegarza4172
This is a simpler problem that doesn’t require substitution, but does a good job explaining the overall concept
It took me 5 seconds to do it
Took me just a flich@@SuperStudiousman
Nah, true chads make it the integral of x^2 + 4x + 4 to get x^3/3 + 2x^2 + 4x + C
fact
now do that for (x+2)^20
@@m.guypirate6900 same stuff u gotta calculate in the end anyway
@@saturapt3229 no it isn't lol
Just use Pascal’s triangle lmao but good luck finding the coefficients
You don't even need u-sub. Its a linear function with coefficient of 1, so du will just equal dx.
i think the point was for it to be an easy application of U sub. to make it easier to understand for beginners
Yeah but u sub is easier in this case
That's a shortcut for u-sub that only works in special cases. So when you use that shortcut, you _are_ using u-sub. Just like how the method of evaluating rational limits at infinity is just a shortcut for L'Hopital's Rule that only works for certain types of rational/radical functions.
But yes, you're right, you don't explicitly have to do the working for it, but this channel was made for beginners.
Exactly, That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel.
This is amazingly simple process and so much saving.
This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply.
No more unnecessary steps as part of a long and tedius process.
Yeah but when co efficient isn’t 1?
you don't even need to use substitution for such a simple problem like this, just know that for (x+a)^n, with a being a constant and n being a whole number(negative or positive integer, both work), by integrating you always get [(x+a)^n+1]/(n+1), it's just a simple derivative
i'm sorry but my inner calculus is screaming PLUS CEE
Correct.
[(ax + b)⁽ⁿ ⁺ ¹⁾]′ =
a(n + 1)(ax + b)ⁿ
How would you answer the next question:
● Find the primitive function F(x)
(i.e. F(x)= ∫f(x)dx) of f(x) = (ax + b)ⁿ
(‼️whithout using the standard list of primitive functions.‼️)
where x is in the Domain
D ⊆ ℝ of f and n ∈ ℤ.
That is just because of the use of a U-Sub implicitly, this shows out the steps for that formula. Don’t remember a formula blindly without understanding it’s derivation
I’m pretty sure that’s already what U substitution is, it’s just giving a formulaic way of solving it.
kid named reverse chain rule then divide by derivative:
derivative named kid:
@@XanderAnimations lmaoo
My maths teacher always used to tell me that if it's a linear function in x then integrate it as you would just f(x) then divide by coefficient of x
yup, because
if
∫ f(x) dx = F(x) + c
then
∫ f(ax+b) dx
{u=ax+b, du= a*dx, dx=du/a}
= ∫ f(u) (du/a)
= (1/a) ∫ f(u) du
= F(u)/a + c
= F(ax+b)/a + c
Some people need long solutions and some don’t. This helped with integration of (a-x)^-2. Thank you.
Me watching this:-😵💫😵💫
If this channel existed when I was preparing for my calculus exams 20 years ago, I think I would have gotten much better grades!...
But TH-cam ITSELF wasn't launched until 2005, so TH-cam didn't exist at all when I was in university.
Thanks for making me feel old. 😜
No, but seriously, thanks for these videos!
You must be helping the next generation.
Excellent explanation 👍🏽🔥
Thank you very much, I was stuck on a problem like this today :D very good short!
Are you in high school?
Thank u 😭I've been trying to figure out the step after getting the u 😭
Me too
You are the good Physicist!
idk why i but i lowkey find u sub fun and interesting to learn
Now integrate √(x²+2x)
2/3 * 1/2x+2 *(x^2+2x)^3/2
U can use the reverse chain rule aswell ( faster u sub )
In general, integral of
f(ax+b) = (1/a)*F(ax+b)
I never learned this in school this is my first time
My prof will give an "❌" for that answer
Okay so this helped me A LOT. Coming back to school (2 yrs) after being sent across seas and been thrown into a calc 2 class… I remember some things but the really helped me out!!
Thank you
You're the best rapping in math explaining congrats
thanks bro
dx = d(x+2)=dt
Int (x+2)dx = (x+2)^2/2 + const
Thanks!!!!
Just use the reverse chain, substitution is not needed for problems like these
Question:
Is the reverse chain implicitly the u-sub approach?
U-sub is the reverse chain lol
Please make more of these
Ok ok i subscribed. U earned it!❤
Using the second fundamental theorem of calculus is clearer , just find the derivative of (x+2) , which is 1 , then mould it properly. Then you get the answer
Simplier without sub because we always can add const in differential: dx = d(x + const)
Not a speedrun at all. Just notice the derivative of that is 1, then treat (x + 2) as if it was what you’re integrating, and (1/3)(x + 2)^3. Should take you 1 or 2 seconds to solve
Math is so difficult nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai 😢
The multiplying of both sides by dx caused me physical pain... smh
Why?
Oh I just develop the square of the binomial and integrate every term, but your metod it's Very good, if it is something basic, it should be noted that I am just learning to derive/integrate, so I don't know a lot of
It's genuinely easier to just do it as it is
True, but this is a good demonstration of using substitution to solve the integral.
For this specific method, we can just simply use antiderivative.
i found it before the video even started
X³+x²+4x+c
Why is bro making this simple problem so complex? 😂
to teach? imagine it was something more complex u could apply same u sub
You didn't need the du/dx, you could directly go ahead and substitute the u for x+2 and still get the same answer at the end. You made it way more complicated than it qctually is dude.
My fellow idiot. You need to substitute dx with du. That's why he did ask the calculation.
Wait till trigo functions get involved
Day 1: Manifesting Desire
Day 2:
"first we need to find you"
PLEASE DON'T FIND ME!! I HAVE A FAMILY!!!!
just expand the x+2 to get the integral of x²+4x+4
“I don't integrate the question, l differentiate the
options”
~Ме
Everything on TH-cam calculus makes sense BUT when I get in class I’m dumb 😊
I did a question like this in the same way coz my dumbass forgot there is a simpler rule for linear equation with exponents
Don’t memorize, think
People will hate on me for this but i do not care. I never liked U sub and never will. I understand the concept and instead just solve the integral using the tabular table instead.
or just write it as the derivate of ((x+2)^2)/2 so thats about it , u sub is used for problems that are so easy to use just directly
du=dx so u sub isn’t necessary so you get 1/3(x+2)^3 +C or just expand it like normal people.
Just use reverse chain rule, and you find out that you divide by 1 (because of the coefficient of x), so you simply have to use the reverse power rule.
That's what u-substitution is.
Sometimes U-sub is helpful sometimes it's superfluous.
It’s tough for me figuring out what “u” is
3)
2
(2x)dx = ∫ [ f(x)]
2
f ′(x)dx = 1
3 ∫ [ f(x)]
3
+ c
= 1
3
(x2 + 3)
3 + c
There is no need for u sub. Make the 2 a then take that number flip it as if it was a fraction and multiply it to the front. Add c ofc.
Another way is reverse chain rule
we still can't solve the integral of some basic mathematical functions
For example, although we can calculate the result of the integral e^sin(x) dx numerically, we cannot express it symbolically. Mathematics is not a science, it is a language. #math #mathematics #integral #sinus #cosinus
yeah I'm taking AP Calc AB next year and It is wraps.
Man just add one to the power and divide by the new added power man making it so hard
Just (x+2)^3/3+C
Just expand the bracket and integrate lol
n i c e
Like in chain rule in differentiation when you multiply the derivative
Why not divide the derivative in integration in this problem
Ok, this is impressive. now explain partial integration in 60s 🤣
Math was easy before meeting calculas😂
No one has ever heard of
Integrate f(x) dx
=
Integrate f(x) d(x+a)
And
Integrate f(x) d(kx)
=
k * Integrate f(x) dx
Seriously nobody???
No need for substitution.
Bro made something so easy complicated
Just find the anti-derivative then you’re done
(x-2)^3
----
3
that only works in very simple problems like this one
In normal way, by expanding (x+2) ^2 and integrating we get : ((x^3) +(12x) +(6(x^2))) /3
But through substitution method :
((x^3) +8+12x+(6(x^2)) ) /3
An additional 8 is coming!!!!!!
Iam so confused.
Can anyone explain plz 😢!!
how did I get here... what the fuck is an integral?
Plenty of alternatives. If you really wanted to waste your time, this can be done by parts.
I did calculus and the moment this all made sense was when I realised theirs who du de dx bullshit was what was confusing me😂
t²dt
= t³/3
= (x+2)³/3
I sub
Just use power rule
What I tell my students:. U-sub is the Swiss army knife of integration techniques! 😃
This is because you were taught one way as you teach only one way. As if it were the only way. Sadly it's the only way you know and you provide so little worth to your students while you mimmic parrot as a career. Hero to no one.
im gonna cry
(ax+b)^n has a formula use it
wow.. though there's a short way out to tackle it
Look I understand it to an extent but slow down 😂
Isn't this more useful when numerator is the derivative of the denominator?
Where does the two other dx in the du=dx come from?
how this method can solved real world problem?
Lol just expand it and integrate each piece. Its only a quadratic, if the power was 3 or above then I would use a u sub
Calculus seems so difficult, like what is this even for fr
Give it time once you get into more advanced math you will realize how everything connects
This is like one of the most basic integral questions, what are you talking about?
@@nickronca1562 I just don’t know, like what is it for
@@Zane_Ritchie Integrals are for finding the area under the curve of some arbitrary function f(x).
For example if you have the speed function of some object, you can get its distance
Can you pls explain where did U come from?
It's just a placeholder to make the calculation simpler.
@@420sakura1 Thank you! Ohh so it doesn’t have any value it’s just like a bracket? (Me don’t know anything me in 8th st.)
@@vaishalikarande3246 don't worry, you will learnt all these and more in 2-4 years. Remember the derivative and integrals by heart. It is essential in Univeruty regardless which stream you choose.
Thank you so much for your fast reply and tips 😊😊!!
what is this pre calc
(x+2)³/3 is right but not easy to calculate when x number
Not possible this answer check differentiate the integrated answer
Why use a U substitution? its a simple derivative?
i like u
If derivative of inner function is 1, no need to do u sub
if this is how u americans be doing calculus, no wonder you guys find it so hard 💀
?
That is why we are good at it more like it
Americans?
But you can just expand lol
oh what the actual fuck
Just use reverse chain rule it’s faster
I can't believe that I finally found someone who said this. I hate it so much when people use u-sub for such simple integrals like this one.
its the same
reverse chain rule is just the consequence of a u-sub that always works:
if ∫ f(x) dx = F(x), then:
∫ f(ax+b) dx
{u=ax+b, du= a*dx, dx=du/a}
= ∫ f(u) (du/a)
= (1/a) ∫ f(u) du
= F(u)/a
= F(ax+b)/a
see
They are the same thing lol
U was completely unnecessary lol, this is just the power rule of anti derivatives
I'm in 8th grade but I was screaming saying just evaluate the integral as it is omg no need to use U Substitution for an equation like this
U-sub? More like “U deserve more subs!” 👍
So bad
@@gamerfanletsplay9302 Then my work here is done. But if you ever want to hear a pun on a particular topic, just let me know and LetsPlay!