How do you find the volume of the solid generated by revolving the region bounded by the curves y=x^2, y=0 x=2 rotated about the x-axis?

1 Answer
Aug 30, 2015

See the explanation.

Explanation:

A at a value of x in [0,1}, a representative disk has radius "top "y - "bottom "y which will be x^2-0=x^2

Th volume of a disk is pi r^2 * "thickness".

The thickness in this case is dx

Volume of slice: pi(x^2)^2 dx

Volume of the solid int_0^1 pi(x^2)^2 dx

We need:

piint_0^1 x^4 dx = pi [x^5/5]_0^1

= pi[(1)^5/5 - (0^5)/5]

= pi/5

The volume is pi/5