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Problem 2 Medium Difficulty

Find the volume of the solid obtained by rotating the region bounded by the given curves about the $x$ -axis. Sketch the region, the solid, and a typical disk or washer.
$y=1-x^{2}, y=0$

Answer

$\frac{16 \pi}{15} \approx 3.351032165$

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Video Transcript

a base of discretion. We have to find a whole human for a soul of revolution between the curves Why is equal to one minus X squared Y is equal to zero on the X axis. So if you were to draw Big Sketch So this is the line. Why is equal to zero by zero, which is the X axis and this is one minus X squared. This is one minus X squared. So we have to basically imagine this revolving around the X axis and invisibly forming a sphere. So the volume for soldier of revolution is the integral between X is equal to negative one on one over one minus X squared DX. This is equal to X minus X huge over three. I'm gonna evaluate this from naked. I wantto one, This is one minus 1/3. That's one minus 1/3 minus negative one minus negative, one over three months, plus one over three. So therefore, our final and Zaheer, don't forget, we also multiplied by pi. There's a pile on the outside. So our final answer here is equal to 16 over 15 over 15 multiplied by pi