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Find the Volume of a Solid by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

\(\displaystyle x = y^2\), \(\displaystyle x = 1 - y^2\), about \(\displaystyle x = 3\)

So here is how far I've gotten with this problem. I need help though. Any guidance will be greatly appreciated.. One of the problems is I don't understand what "about x = 3" means exactly? Like what do they mean "about x = 3?" Anyways here is what I have:

I have a right and left parabola basically. I set the two equal to each other to find lines of intersection.

\(\displaystyle

y^2 = 1 - y^2\)

thus;

\(\displaystyle y = \frac{\sqrt{2}}{{2}}\)

So I know the areas are even symmetry so I can say \(\displaystyle 2\pi \int^\frac{\sqrt{2}}{2}_0 (Right - left)dy \)

right?

so am i correct in saying \(\displaystyle 2\pi \int^\frac{\sqrt{2}}{2}_0 (1 - y^2)^2 - (y^2)^2 dy\)?

\(\displaystyle x = y^2\), \(\displaystyle x = 1 - y^2\), about \(\displaystyle x = 3\)

So here is how far I've gotten with this problem. I need help though. Any guidance will be greatly appreciated.. One of the problems is I don't understand what "about x = 3" means exactly? Like what do they mean "about x = 3?" Anyways here is what I have:

I have a right and left parabola basically. I set the two equal to each other to find lines of intersection.

\(\displaystyle

y^2 = 1 - y^2\)

thus;

\(\displaystyle y = \frac{\sqrt{2}}{{2}}\)

So I know the areas are even symmetry so I can say \(\displaystyle 2\pi \int^\frac{\sqrt{2}}{2}_0 (Right - left)dy \)

right?

so am i correct in saying \(\displaystyle 2\pi \int^\frac{\sqrt{2}}{2}_0 (1 - y^2)^2 - (y^2)^2 dy\)?

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