Question

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.

Answer 1

idk

Answer 2

lolz

Answer 3

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 ?

Answer 4

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

Answer 5

oops, I meant dy

Answer 6

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

Answer 7

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

Answer 8

once you integrate it you are done :)

Answer 9

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