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Find the volume generated by revolving the regions bounded by the given curves about the $x$ -axis. Use the indicated method in each case.$$y=x^{2}+1, y=x+1 \quad \text { (shells) }$$

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 3

Volumes by Integration

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:21

Use the shell method to fi…

02:56

02:04

01:06

Find the volumes of the so…

0:00

Use the method of cylindri…

01:16

01:18

00:59

02:12

So in this problem we need to find the volume generator. Well my wife is equal to X squared and were given that. Why is equal to experts? one also. So if you go ahead and drive the functions here graft into bikes. But first of all let y be the radius of the shell and execute the height. Next is the height of the height and b y is the thickness of the shell. So by the method of cylindrical shells, the volume of thera presented shell will be equal to D. C. Equal to two pi times the radius times the height, times a picnic. So the total volume of the southern um with the Kirby involvement from Y is equal to A. So why is he puts a B. We'll take the integral of the volume. So these equal to two pi times the integral of DV with a linear speed A and B. So this becomes two pi times the radius times so hard. Times of deafness song substituting the value of the radius, thickness and height. We get We are two pi times the integral of with the limits. Andy Yeah. Why times X times that's why. So the elements of the area that generates the show On my secret zero. Otherwise, okay, once we take the integral since y is equal to x cubed and access equal to Watch to the 1/3, we can substitute the values for why an act To our integral. So we have two pi times why Still up for 3rd do you want man? 12 y to the 4th, 3rd. Just Watch to the 7 3rd Over 7/3 tom two pi With limits being zero and 8. So this gives us the volume to be equal to 768 5, divided by myself.

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