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## Homework Statement

The solid formed when the region bounded by y = x^2 and y = 2 - x^2 is revolved about the x-axis

## Homework Equations

disc method with respect to x-axis

the integral of : (pi * (f(x)^2 - g(x)^2))

## The Attempt at a Solution

When I square each function and integrate the resulting difference I get :

4x - 4x^3/3 with limits of integration from 0 to 1 (x = 0 and x = 1)

My final answer is 8pi/3 (eight pi thirds)

My solutions manual gives me an answer of 16pi/3. However, I noticed that they have a constant factored out of their integral of 2pi instead of just pi. You are supposed to use pi instead of 2pi for the disc method, hence their answer being exactly double what mine is.

Either this is a mistake on my book's part or I am missing something :(

Please help!