Question

Sketch a plane region and indicate the axis about which it is revolved so that the resulting solid of revoltuion (found using the shell method) is given by the integral.

π
2π∫ xsinx dx
0

Answer 1

See attached picture.

Explanation:

The idea of the shell method is to find the volume of a differential shell by using the formula:

`V=2\pi\int\limits^a_b {rh} \, dr`

in the drawing we can see that r=x, h=sin x and dr=dx. The area is revolving about the y-axis from x=0 to
`x=\pi`. So the volume is found by using the following integral:

`V=2\pi\int\limits^\pi_0 {xsin x} \, dx`