Area Between Two Curves

[@TheOrganicChemistryTutor]

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: kzbin.info/www/bejne/jZ6lq6B-p9pqbtk

[@nelsonikechi8316]

Good

[@miako-chan999]

Thx bro 😅😊

[@gelina2650]

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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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

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[@georgesadler7830]

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 KZbin TV with the Organic Chemistry Tutor.

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[@brechttanghe9769]

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.

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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

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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.

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@@SB-qh6cr I thought f(y) would be the right function and g(y) would be the left function?

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[@stevenkazze1207]

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"?

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@@austina.c.3532 don't get it explain please

[@amirandd3658]

This video help me to calculate area under the graph

[@hamaadsiddiqui8927]

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

[@madghostek3026]

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

[@madghostek3026]

I see later examples dont care about sign either, maybe depends if you allow negative area or not...

[@josephmonte1470]

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.

[@hamaadsiddiqui8927]

@@josephmonte1470 oh okay that makes sense thanks

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15:22 19:00 26:00 31:27

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4 hrs before the test 😊

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[@aleksandaratanasovski7618]

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)

[@evanmckeand6678]

30:08 why did you flip the function from x^2 -4x to -4x- x^2?

[@evanmckeand6678]

X^2-4x to -4x - x ^2

[@evanmckeand6678]

Nevermind!

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[@ahola9338]

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?

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@@priyankapaani2930 wasn't too bad, much better than I expected

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@@aaperm6566 good to hear...did you take at school or digital exam?

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Isn't f(y) at 2:36 not a function? Because I can tell it wouldn't pass the vertical line test.

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Idk why you guys are here but I enjoy physics. With only a highschool education I can somewhat grasp the algebra shown without paper. Pretty fun...

[@zabhizebest9891]

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??

[@HMUP7]

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 :)

[@HunterGallagherGL2]

@@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?

[@HMUP7]

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.

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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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@6:25 mark can you explain why you did 2x^2/2

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