Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK Direct Link to the Full Video: bit.ly/3DGVcYy Full 2 Hour Video on Patreon: www.patreon.com/MathScienceTutor Calculus 1 Final Exam Review: th-cam.com/video/WmBzmHru78w/w-d-xo.html
within 4days, you and you channel has helped me understand my entire syllabus (Differentiation, Integration and Standard Deviation) from nothing. i got my results today and i scored whopping 109/120. where as i would probably have failed. I will forever be grateful to you. i cant thank you enough for what this channel has done for me and that also for free. i hope one day i am able to contribute to your patreon, You are doing gods work and i pray you have a prosperous and healthy life.
0:14 = Area from a to b (vertical strip) 2:25 = Area from c to d (horizontal strip) Example problems: 4:20 (1) Calculate the area bounded by the region by the line y=8-2x, the x-axis, and the y-axis 9:41 (2) Calculate the area of the region bounded by the line y = x and y=x^2 13:25 (3) Calculate the area of the region bounded by the curves y = x^2 and x = y^2 19:40 (4) Calculate the area of the region bounded by the curves x=1-y^2 and x=y^2-1. 24:51 (5) Calculate the area of the region bounded by the line y = x^2-4x and the x-axis. 31:22 (6) Calculate the area of the region bounded by the equations y=x^2-4x and y = 6 - 3x. 39:35 (7) Calculate the area of the region bounded by the equations x= 3y-2
Professor Organic Chemistry Tutor, thank you for a fantastic video/lecture on finding the Area Between Two Curves in Calculus Two. Graphing the function/functions is very important when finding the Areas Between two Curves in Calculus. All the examples are off the learning charts in this great video. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
I wish I could see this person and thank him for everything. He is literally everything. I mean, nothing in this this whole world is hidden in his powerful brain.Keep the good job sir 👏 and where are you from ?
I watch this teacher before I attend the class. It makes the world different in my understanding the concept of calculus. His explanation is better than some of my former Professors. Thank you very much for making the different in my learning.
I am currently studying for my calculus test and your longer videos with all these practice problems have been so helpful to review all the material! I can't thank you enough :)
When I watch the lectures of our prof at the uni, I get hopeless and depressed depressed and then I watch a 15 mins vidoe of OGT, I am a supermath at least super enough to make my homework :) He should get an award, this channel is a social project💯
First you need to know the concept of limits, then you need to know how to take the derivatives of functions, then you need to know how to do the reverse (anti derivatives), then with anti derivatives you can find integrals and that’s the only calculus part in this specific lesson
For number 4 at 17:40 Once you know the shape of the curve of x=1-y^2, you can just rotate it 90° and calculate the area of y=1-x^2 from -1 to 1, after that multiply it by 2 (because x=y^2-1 is mirroring x=1-y^2) and you get the same answer, just alot faster if you're used to x-curve calculations. It's quicker, better if your exam is time bound.
You make difficult things more understandable and simple things more simpler. I prefer to watch your videos in every lesson and even encourage my classmates to watch your videos.Good job always, your friend from Papua New Guinea
I love the way you give different examples...and love the way you explain the graph....you pay so much attentions to it ...which some tutors won't do..😊
You are already his student. Just look how many people give up on their professors and come here to watch his content instead and end up learning more effectively.
If someone can. How do I know which function is f(x) and which is g(x), how do I tell the difference? Or is it always that the right function given in the problem is f(x)? (example in the fourth problem how do I tell the difference)
Sir...I just want to see your face and wanna Thank you for doing such a great work.....😇😇 And Also I wanna ask you a question that how do you know that we need this chapter ?🤔
f(x) is the top function and g(x) is the bottom function. and if the function requires left or right f(x) is the right function, while g(x) is the left one.
You such an legend sir but its unfortune that some of us can't afford full video since we are student depending on bursary for our tuition fees and other.
제가 흔히 봐왔던 그래프는 y가 종속변수이고 x가 독립변수인 꼴의 그래프였습니다. 공부를 함에 있어서 점점 많은 형식들이 이러한 종속변수와 독립변수의 개념이 모호해지고 그러한 적분을 수행해야할 때가 많았는데 그러한 적분방법의 기초를 이 영상을 통해 다시 상기할 수 있었습니다.
What area are you solving for if you subtract the grater function from the lower function? Or in the y-axis, the righter function from the lefter function?
I think this is solved wrong, the basic f(x)-g(x) formula fails here, normally the goal is that youre subtracting smaller area from bigger, so you get a floating strip, but you can't just do that when it crosses X axis. You should find parts of the area that are under Y=0 and treat them as negative (just place - in front of integral I guess), here everything is under Y=0. Try solving area between Y=2 and Y=-1 and it will become clear
In these examples we are being asked to solve for the area of a shaded region, also know as area of a region bounded by curves. If you were simply evaluating an integral and being asked to compute the net area then that would be the case.
This might be dumb question but let's say I have no clue on how the graph looks like, how can I know which function if the f(x) and which is g(x).... Because don't it change the area when you subtract??
you wanna set them equal to each other and then solve for the variable, then plug in a test number that is between the values you obtained ( between [a,b] ) and that value should tell which function is bigger :)
If you know your graph, that's better! You wanna look at your graph and see the bounded region, then you wanna see which function is on top and which one is on bottom. Ideally, that can be found easily from just looking at the graph. However, if they were functions of y, then you would want to mark them as right and left not top and bottom. Right and top are always the bigger functions.
Graph on right side f(y) left is g(y). Graph on the top is f(x) , bottom is f(y).if you want to know how to draw Graph may be his curves lecture on calculus would help you.just check it
Hey, thanks a lot for the videos and explanations. I got a doubt, as in the 5th exercise. By convention and notation, this area falls under the x-axis. Must the result be expressed as a negative number, supposing that's "the area above the graph"?
Hey! I am also an Chemist. And I love to read physics thats where your videos are helping me a lot. Shall I share one calculus problem with you ? Thank you.
f(x) is typically the function that bounds your region at the top, and g(x) is typically the function that bounds your region at the bottom (at least when working in terms of x). This is why drawing a picture of the region is helpful. If you are interested, I explain this in detail with plenty of examples in my own video on this topic, I'll link it here for you. Hope this helps! Link: th-cam.com/video/KrpAZnnx0uM/w-d-xo.html
Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK
Direct Link to the Full Video: bit.ly/3DGVcYy
Full 2 Hour Video on Patreon: www.patreon.com/MathScienceTutor
Calculus 1 Final Exam Review: th-cam.com/video/WmBzmHru78w/w-d-xo.html
Good
Thx bro 😅😊
within 4days, you and you channel has helped me understand my entire syllabus (Differentiation, Integration and Standard Deviation) from nothing. i got my results today and i scored whopping 109/120. where as i would probably have failed. I will forever be grateful to you. i cant thank you enough for what this channel has done for me and that also for free. i hope one day i am able to contribute to your patreon, You are doing gods work and i pray you have a prosperous and healthy life.
0:14 = Area from a to b (vertical strip)
2:25 = Area from c to d (horizontal strip)
Example problems:
4:20 (1) Calculate the area bounded by the region by the line y=8-2x, the x-axis, and the y-axis
9:41 (2) Calculate the area of the region bounded by the line y = x and y=x^2
13:25 (3) Calculate the area of the region bounded by the curves y = x^2 and x = y^2
19:40 (4) Calculate the area of the region bounded by the curves x=1-y^2 and x=y^2-1.
24:51 (5) Calculate the area of the region bounded by the line y = x^2-4x and the x-axis.
31:22 (6) Calculate the area of the region bounded by the equations y=x^2-4x and y = 6 - 3x.
39:35 (7) Calculate the area of the region bounded by the equations x= 3y-2
Thank you for this! This is extremely useful when trying to study the problems.
You're a real one for making the time stamps thank you sm
Work of Gods
Thanks!
my savior
Sometimes I wonder how much this guy knows, it seems like he knows everything 🤣😌
If I'm to graduate with a first class, I would dedicate my success to this man
He doesn't disappoint
Maybe he's just making videos as he learns new things.
He just knows what he knows
That time he's even good at teaching too
@@SolidSiren No, pretty sure he's like an AI lead at Tesla or smth. Very smart guy. This is like his side gig.
I really dont need this video right now but i just wanted to say that this channel is the only reason i passed physics last year. Ty
this channel and khan academy are going to carry me through calc 2 and physics, i can feel it
How’d you do bro
@@abaza1646 91 in physics, 88 in calc 2 lol
@@Po_goes_brrr daaaaamnnnn well done man
@@Po_goes_brrr sheesh that’s sexy. I got a DD in Calculus 1 last semester. Hope I can squeeze some more for calculus 2 and keep my scholarship…
@@sirpomegranate2446 did u keep it?
You have literally been coming out with these lessons the day I'm being taught them
FRRRR
Half of the world is educated by you 🌹
Exactly 💯
IDK WHAT I'D DO WITHOUT THIS GUY!!!
Same here
You are really a great teacher. I'm learning calculus on my own and all you videos are helping me. Thankyou 🙂🙂🙂
Your videos are always helpful, I rather prefer to watch just a minute of your video than an hour video from another channel
good
An hour listening to my Prof is torture
@@mathsandsciencechannel delete your channel lmao. We got this channel
@@somxr_738 lmfao
YOU are helping us, we are promoting your page, but academically you are really helping the world. Love you , I believe you know everything
Professor Organic Chemistry Tutor, thank you for a fantastic video/lecture on finding the Area Between Two Curves in Calculus Two. Graphing the function/functions is very important when finding the Areas Between two Curves in Calculus. All the examples are off the learning charts in this great video. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
I wish I could see this person and thank him for everything. He is literally everything. I mean, nothing in this this whole world is hidden in his powerful brain.Keep the good job sir 👏 and where are you from ?
I watch this teacher before I attend the class. It makes the world different in my understanding the concept of calculus. His explanation is better than some of my former Professors. Thank you very much for making the different in my learning.
I am currently studying for my calculus test and your longer videos with all these practice problems have been so helpful to review all the material! I can't thank you enough :)
awesome, hope you will pass you test. Stay curious
I just want you to know you're actually the goat bro. Out here saving lives.
When I watch the lectures of our prof at the uni, I get hopeless and depressed depressed and then I watch a 15 mins vidoe of OGT, I am a supermath at least super enough to make my homework :) He should get an award, this channel is a social project💯
Don't understand one thing about this. I won't ever understand one thing about this. I didn't even search for this. I still watched the whole thing.
it's so easy just focus
ask me if you want
First you need to know the concept of limits, then you need to know how to take the derivatives of functions, then you need to know how to do the reverse (anti derivatives), then with anti derivatives you can find integrals and that’s the only calculus part in this specific lesson
I feel your pain
I am 62 and I am able to follow through the lecture easily. Thanks
You helped me so much in school pls drop the merch
For number 4 at 17:40
Once you know the shape of the curve of x=1-y^2, you can just rotate it 90° and calculate the area of y=1-x^2 from -1 to 1, after that multiply it by 2 (because x=y^2-1 is mirroring x=1-y^2) and you get the same answer, just alot faster if you're used to x-curve calculations.
It's quicker, better if your exam is time bound.
You make difficult things more understandable and simple things more simpler. I prefer to watch your videos in every lesson and even encourage my classmates to watch your videos.Good job always, your friend from Papua New Guinea
Bro, you always post these videos right before my finals.
I love the way you give different examples...and love the way you explain the graph....you pay so much attentions to it ...which some tutors won't do..😊
How did you learn so much I mean, you practically know every single topic that I need help with and your explanations are sooooooo gooood.
I dont know how this happen but I needed this video and you uploaded
Brother I really don’t know what I’d do without these vids ❤😊
This teacher can replace the whole Department of Computing and Mathematics😂😂😂😂He's toooo SMART!!!!!!
thank you bro. been working on something for so long. unintentionally you answered my question
Literally the only thing that has explained to me how these problems actually relate to the shape
You are a life savior. Thank you very much for those videos!
I will recommend my lecture to your videos so we can learn together... This is helpful 👏🏾👏🏾
tomorrow's my test and u just posted this yesterday. thank you!
There needs to be a way to have this guy as my teacher
You are already his student. Just look how many people give up on their professors and come here to watch his content instead and end up learning more effectively.
We owe so much Organic Chemistry Tutor 🙏
all your videos are helpful and I often prefer to watch your tutorials.
Yes
Very beneficial channel for free learning. More than thank you to organic science tutor.
Your videos are always on the right time! Thanks
You really deserve everything man am really getting to pass my exams because of u tq tq tq a lot
This dude should be given award!
I don't know how I can show my gratitude to u,any way u are blessed bro and always remember to be grateful for the gift which GOD gave you.
The most great teacher ever🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉
Thank you for posting. This is my first comment as I joined you three days ago.
I joined 2 days ago an its helped so much in such little time
@@airadaisies3390 100%
Thanks a lot !!!! your teaching method matches for me.
i have finals this week, time to binge watch all of your calc videos...lol
I have a Baccalaureat examen next Tuesday :(
@@hafsaghounoune7354 good luck!!!
@@abigailmartin26 Thank you !
@@hafsaghounoune7354 lol me 2
Thanks so much...I owe you my degree🔥
Your videos are so much helpful 💗
Thank you 💗
17:22 I don't understand how did you solve that
Long video but worth it
Thanks for the info!
Really appreciate it!
Awesome teaching!
coming to his channel after every calculus 2 lecture to try and understand what in the fuck im doing
I love you so much and I love your videos they always help me for my calculas exams
My mentor ! Keep it up.
After watching my professors videos I didn't understand a single thing. After watching this video I understood everything.
Best. i watched a lot of videos but it was the best😭
Why is this man the Goat?
Indeed we are blessed to have you.
I have my calculus final tomorrow !!!! The very last paper !!!! ✨🫶🏾 praying I do well ❤️
best tacher in calculus thanks
thank you so much brother.
i have an exam tmr and my teacher explained this topic really badly. this saved me so much, thank you.
You are best teaching
I like your videos, they are so helpful
Your videos are always helpful
If someone can. How do I know which function is f(x) and which is g(x), how do I tell the difference? Or is it always that the right function given in the problem is f(x)? (example in the fourth problem how do I tell the difference)
ty for your info Sir! much needed help
Sir...I just want to see your face and wanna Thank you for doing such a great work.....😇😇 And Also I wanna ask you a question that how do you know that we need this chapter ?🤔
4 hrs before the test 😊
Still confused which one will be the f(x) and g(x) but thank you mister this is much better than my professor's 2 hour lecture
f(x) is the top function and g(x) is the bottom function. and if the function requires left or right f(x) is the right function, while g(x) is the left one.
@@SB-qh6cr this is so helpful thank you
@@SB-qh6cr I thought f(y) would be the right function and g(y) would be the left function?
@@SM-qn7sr yeah thats correct, i'm just used to thinking functions in terms of x, so i just use "x". It should be in terms of "y" tho!
Helpful as always :)
OMG THANKS ALOT I LEARNED IT FINALLYYY!
This video help me to calculate area under the graph
You such an legend sir but its unfortune that some of us can't afford full video since we are student depending on bursary for our tuition fees and other.
15:22
19:00
26:00
31:27
제가 흔히 봐왔던 그래프는 y가 종속변수이고 x가 독립변수인 꼴의 그래프였습니다. 공부를 함에 있어서 점점 많은 형식들이 이러한 종속변수와 독립변수의 개념이 모호해지고 그러한 적분을 수행해야할 때가 많았는데 그러한 적분방법의 기초를 이 영상을 통해 다시 상기할 수 있었습니다.
How about writing in English
How do you always upload a video about a problem I was searching for
same
What area are you solving for if you subtract the grater function from the lower function? Or in the y-axis, the righter function from the lefter function?
i love you man
for 31:15, how does the area turn out to be a positive value, I thought it would be negative since the area is under the x-axis
I think this is solved wrong, the basic f(x)-g(x) formula fails here, normally the goal is that youre subtracting smaller area from bigger, so you get a floating strip, but you can't just do that when it crosses X axis. You should find parts of the area that are under Y=0 and treat them as negative (just place - in front of integral I guess), here everything is under Y=0. Try solving area between Y=2 and Y=-1 and it will become clear
I see later examples dont care about sign either, maybe depends if you allow negative area or not...
In these examples we are being asked to solve for the area of a shaded region, also know as area of a region bounded by curves. If you were simply evaluating an integral and being asked to compute the net area then that would be the case.
@@josephmonte1470 oh okay that makes sense thanks
I think he has the world strongest memory, I surrender this guy
no way! no way! we just took this lesson several days ago!
Thankyouu. Iam glad u are in the same planet as ours
Isn't f(y) at 2:36 not a function? Because I can tell it wouldn't pass the vertical line test.
this was an amazing lesson! Thank you!!
He is always amazing in all topic in chemistry, biology, physics and math.
cal text in 5 days, wish me luck. If I pass, its all thanks to you
Thank you so much sir♥️♥️
You the GOAT bro🔥🔥
مشكور العزيز الف رحمة على الثدي الذي رضعته
This might be dumb question but let's say I have no clue on how the graph looks like, how can I know which function if the f(x) and which is g(x).... Because don't it change the area when you subtract??
you wanna set them equal to each other and then solve for the variable, then plug in a test number that is between the values you obtained ( between [a,b] ) and that value should tell which function is bigger :)
@@HMUP7 How do I just figure out which one is f(x) and which one will be g(x) when I do know what the graph looks like?
If you know your graph, that's better!
You wanna look at your graph and see the bounded region, then you wanna see which function is on top and which one is on bottom. Ideally, that can be found easily from just looking at the graph.
However, if they were functions of y, then you would want to mark them as right and left not top and bottom. Right and top are always the bigger functions.
Graph on right side f(y) left is g(y).
Graph on the top is f(x) , bottom is f(y).if you want to know how to draw Graph may be his curves lecture on calculus would help you.just check it
Hey, thanks a lot for the videos and explanations. I got a doubt, as in the 5th exercise. By convention and notation, this area falls under the x-axis. Must the result be expressed as a negative number, supposing that's "the area above the graph"?
30:08 why did you flip the function from x^2 -4x to -4x- x^2?
X^2-4x to -4x - x ^2
Nevermind!
Ur an incredible teacher
THANK YOU SO MUCH.❤
Your brain is so big idol😯, sana all😂
Hey! I am also an Chemist. And I love to read physics thats where your videos are helping me a lot. Shall I share one calculus problem with you ?
Thank you.
this comment is underated cant believe nobody got it.
@@austina.c.3532 don't get it explain please
I just finished my AP calculus exam yesterday, please don't pop out on my recommended 🥰💅🧚🏼♀️
Hey, how did it go? Was that hard or easy???
@@priyankapaani2930 wasn't too bad, much better than I expected
@@aaperm6566 good to hear...did you take at school or digital exam?
You’re the BEST ❤
ALL I NEEDED FOR COLLEGE
which line of two should be f(x), respectively g(x), what defines them
f(x) is typically the function that bounds your region at the top, and g(x) is typically the function that bounds your region at the bottom (at least when working in terms of x). This is why drawing a picture of the region is helpful. If you are interested, I explain this in detail with plenty of examples in my own video on this topic, I'll link it here for you. Hope this helps! Link: th-cam.com/video/KrpAZnnx0uM/w-d-xo.html
@@JKMath bless you
My teacher never thought this, it’s 2 hours before the exam and this is on one of the practice tests. Rip