Area Between Two Curves
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- Опубликовано: 11 окт 2024
- This calculus video tutorial provides a basic introduction in finding the area between two curves with respect to y and with respect to x. It explains how to set up the definite integral to calculate the area of the shaded region bounded by the two curves. In order to find the points of intersection, you need to set the two curves equal to each other and solve for x or y. You need to be familiar with some basic integration techniques for this lesson. This video contains plenty of examples and practice problems.
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Good
Thx bro 😅😊
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
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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 RUclips TV with the Organic Chemistry Tutor.
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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.
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The only reason you wouldn't be able to understand the video is if you don't know the pre-requisite concepts going in. None of the pre-requisites are difficult to understand.
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
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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.
Literally the only thing that has explained to me how these problems actually relate to the shape
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This video help me to calculate area under the graph
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!
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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.
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Helpful as always :)
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17:22 I don't understand how did you solve that
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15:22
19:00
26:00
31:27
very useful, thanks
thanks mate
👍
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?
This video is great ty
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: ruclips.net/video/KrpAZnnx0uM/видео.html
@@JKMath bless you
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"?
coming to his channel after every calculus 2 lecture to try and understand what in the fuck im doing
Thank you so much sir♥️♥️
Thank you
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
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مشكور العزيز الف رحمة على الثدي الذي رضعته
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Ple solving determine the area below f(x)=3+2x-x^2 about x axis.
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@@priyankapaani2930 wasn't too bad, much better than I expected
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