(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the volume of a solid bounded by the functions y=1-x^{2}and y=0 revolved around the x-axis

2. Relevant equations(don't know how to show integrals)

A=Pi * the integral from x_{a}to x_{b}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-x^{2}was greater along this interval.

So, V=Pi* the integral from -1 to 1 of (1-x^{2})^{2}dx.

After FOIL I get 1-2x^2+x4. The integral of this polynomial is x-(2/3)x^{3}+(1/5)x^{5}. 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.

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

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