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anonymous
 5 years ago
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.
anonymous
 5 years ago
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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Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0so 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 ?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0if you see that the volume of each ring(washer) has a volume V = 2pi ( (4sqrt(y2))^2  (4(y8))^2) dx so the integration will be\[2\pi \int\limits (4\sqrt(y2))^2 (4(y8))^2dx\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0now all you have to do is to figure out the limit of integration

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0the bottom of the parabola starts at y = 2 and it ends at y = 11 so the limit of integration is from 2 to 11

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0once you integrate it you are done :)

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0If you would like, try using the shell method, which is also a good choice for this one :)
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