# Volume of a solid between 2 functions revolved about the x-axis

1. Sep 3, 2011

### sakau2007

1. The problem statement, all variables and given/known data
Find the volume of a solid bounded by the functions y=1-x2 and y=0 revolved around the x-axis

2. Relevant equations (don't know how to show integrals)
A=Pi * the integral from xa to xb of [f(x)]2-[g(x)]2

3. The attempt at a solution
First, to find the lower and upper x-bounds, set the functions equal to one another to get their points of intersection. You get x = 1 and -1.

To find which function is f(x) (the greater values), pick a test point between -1 and 1. I used 0 and found 1-x2 was greater along this interval.

So, V=Pi* the integral from -1 to 1 of (1-x2)2 dx.
After FOIL I get 1-2x^2+x4. The integral of this polynomial is x-(2/3)x3+(1/5)x5. I then evaluated this by plugging in 1 and subtracting when I plug in -1.

I get 16pi/15. Unsure if this is correct. Would like if someone could check my work.

2. Sep 3, 2011

### Dick

Looks fine to me.