LEARNING GOAL: to compute volume of a solid by using the...

LEARNING GOAL: to compute volume of a solid by using the Washer Method. 6. Find the volume of the solid formed by rotating the region between the curves $y = x^2 + 1$ and $y = 9 - x^2$, about the axis $y = 10$.

Transcript

00:01 So, we are given that y is equal to x and y is equal to x square are the bounded regions.

00:16 So by revolving them, we just have to express the volume of solid generated if in the first a part, the first about the x axis and the second about the y axis by using in the a part as according to cell method.

00:39 So, let it started with the solution.

00:43 So, first of all we are writing it down for the cell method that means by using that cell method, the volume generated can be given as let's say v is equal to integral a to b to x y into the bracket y t of y minus f of y dy.

01:14 So, let's plug in the required values.

01:18 So, if you say the value of y.

01:20 So, x is equal to y, but here x should become equal to under root of y which representing g of y and this representing the f of y.

01:31 Substituting this here, so integral will go from the initial limit will be 0 and the final limit will be 1 and here it should be a 2 x y into the bracket under root of y minus of y dy.

01:46 And hence, therefore, the required volume generated v should be equals to 0 to 1 2 x y into the bracket under root of y minus of y dy.

02:00 So, this is the answer for one of the part of a.

02:07 Similarly, in the same a part, we have to state the volume about y axis.

02:14 For that, we can directly write down it as integral of 0 to 1 2 x y into the bracket g of x minus f of x.

02:28 So, this we can write down as v is equals to by shell method integral a to b 2 x y into the bracket g of x minus f of x dx.

02:44 So, let's plug in the values...

Question

LEARNING GOAL: to compute volume of a solid by using the Washer Method. 6. Find the volume of the solid formed by rotating the region between the curves $y = x^2 + 1$ and $y = 9 - x^2$, about the axis $y = 10$.

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