How do you find the volume of the solid obtained by rotating the region bounded by y=x and y=x^2 about the x-axis?

1 Answer
Apr 24, 2018

V=(2pi)/15

Explanation:

First we need the points where x and x^2 meet.

x=x^2

x^x-x=0

x(x-1)=0

x=0 or 1

So our bounds are 0 and 1.

When we have two function for the volume, we use:
V=piint_a^b(f(x)^2-g(x)^2)dx

V=piint_0^1(x^2-x^4)dx

V=pi[x^3/3-x^5/5]_0^1

V=pi(1/3-1/5)=(2pi)/15