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The integral in question is the triple integral of x dV over the region E, where E is enclosed by the planes z=0, and z=x+y+3, and the cylinders x^2 + y^2 = 4 and x^2 + y^2 = 9.

Well--- so far in cylindrical coordinates I know the r limits will be from 2 to 3 since the cylinders are in the form x^2 + y^2 = r^2

And the Theta limits will be 0 to 2pi.

The z limits are what are bothering me. I believe the lower z limit will be 0, but the upper one is quite confusing. x+y+3 .... am I correct in assuming this should be written as rcos(theta) + rsin(theta) + 3 ??

Lets just say thats right for now (which i know it isnt ) then I would end up getting an integrand with stuff like cos^2(x) which I know isnt a difficult integral if you use half angles, but it just doesn't seem like it should be this long and difficult. What can I do to change my limits?

Thanks for you help.

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# Having some difficulty with a Trip. Integral in Cylindrical Coordinates

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