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.

1. anonymous

idk

2. anonymous

lolz

3. Yuki

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 ?

4. Yuki

5. Yuki

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$2\pi \int\limits (4-\sqrt(y-2))^2- (4-(y-8))^2dx$

6. Yuki

oops, I meant dy

7. Yuki

now all you have to do is to figure out the limit of integration

8. Yuki

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

9. Yuki

once you integrate it you are done :)

10. Yuki

If you would like, try using the shell method, which is also a good choice for this one :)