Question

Evaluate the integral that gives the volume of the solid by revolving the region enclosed by the graphs y=4x-x^2, x=0, and y=4 around the y-axis.

Answer 1

In the book, it says that the integral would be set up like this:\[2 \pi \int\limits_{0}^{2} x(4-(4x-x^2) dx\]

Answer 2

But I'm not entirely sure why- why do we need to have 4x-x^2 be subtracted from 4?

Answer 3

This is the region I'm finding, right?