Find the volume of the solid formed by rotating the region bounded by: y=x^2+2 and y=x+8 around the line, x=4. Leave the answer in terms of pi.

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Find the volume of the solid formed by rotating the region bounded by: y=x^2+2 and y=x+8 around the line, x=4. Leave the answer in terms of pi.

Mathematics
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idk
lolz
so what you are basically doing is to find the volume of the washer (I usually call it a ring) and integrate it. what do you think the integrand is ?

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if you see that the volume of each ring(washer) has a volume V = 2pi ( (4-sqrt(y-2))^2 - (4-(y-8))^2) dx so the integration will be\[2\pi \int\limits (4-\sqrt(y-2))^2- (4-(y-8))^2dx\]
oops, I meant dy
now all you have to do is to figure out the limit of integration
the bottom of the parabola starts at y = 2 and it ends at y = 11 so the limit of integration is from 2 to 11
once you integrate it you are done :)
If you would like, try using the shell method, which is also a good choice for this one :)

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