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Working on a integral problem and I'm stuck. Revolving around the x-axis seems easy enough, but around the y-axis is giving me trouble for this specific problem.
The region is bound by y=x^2+1 , y=x+1, x=3, and x=6. Around the x-axis I get 1542.6pi, but I'm not sure how to set up the integral for around the y-axis. Do I need 3 separate integrals? The y values run from 4 to 37, so are those my bounds? I was thinking the 3 integrals would be:
from 10 to 37 of (6)^2 - sqrt(y-1) dy
from 7 to 10 (6)^2 - (3)^2 dy
from 4 to 7 (y-1) - (3)^2 dy
Add those up and that's the answer? Thanks for any help, haven't run into one like this in the homework yet.
The region is bound by y=x^2+1 , y=x+1, x=3, and x=6. Around the x-axis I get 1542.6pi, but I'm not sure how to set up the integral for around the y-axis. Do I need 3 separate integrals? The y values run from 4 to 37, so are those my bounds? I was thinking the 3 integrals would be:
from 10 to 37 of (6)^2 - sqrt(y-1) dy
from 7 to 10 (6)^2 - (3)^2 dy
from 4 to 7 (y-1) - (3)^2 dy
Add those up and that's the answer? Thanks for any help, haven't run into one like this in the homework yet.
