Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 5x^2, y = 5x, x ≥ 0; about the x-axis

V = ???

Sketch the region

1 answer

Given the region shown at

http://www.wolframalpha.com/input/?i=plot+y%3D5x^2%2Cy%3D5x

and recalling that the volume of a washer with thickness dx is

pi (R^2-r^2) dx
where R=5x and r = 5x^2

it should be clear.

You can verify your answer using shells, where the volume of each shell is

2pi r h dy
where r = y and h = √(y/5) - y/5