
Integrate the function
Hi, I am kinda having trouble trying to find the limits for the triple integral.
Please help....
Thanks.
Integrate the function https://instruct.math.lsa.umich.edu/...b7704d4671.png over the solid given by the figure below, if P=(4,4,2), Q=(3,3,2), R=(3,3,2), and S=(4,4,2).
integral =
(You should find the actual value when you evaluate the integral!)

Are we to assume the bottom is in the xyplane? Use cylindrical coordinates, of course.
$\displaystyle \theta$ goes from $\displaystyle \pi/4$ to $\displaystyle 5\pi/4$ (arctan(4/4)= arctan(1) to arctan(4/4)), r from $\displaystyle 3\sqrt{2}$ to $\displaystyle 4\sqrt{2}$, and z from 0 to 2.

Thanks a lot for the reply(Clapping)...
I tried to integrate the function and getting 2960/3 which is not the right answer...
okay.. first I converted to cylindrical coordinate!!!
Given, 5x+5y
so 5(r*cos(t))+5(r*sin(t))
now integrated the following function:
=> (5(r*cos(t))+5(r*sin(t)))*r*dz*dr*dt
=> (740/3)*sqrt(2)*sin((1/4)*Pi)+(740/3)*sqrt(2)*cos((1/4)*Pi)(740/3)*sqrt(2)*sin((5/4)
=> 2960/3 (Doh)(Doh)(Doh)

finally..
the answer is 2960/3 ... so I guess its not a volume...(Bow)
Thanks again....

what would make you think it was a volume?

volume!!!
Well, double and triple integral could be volume if( f(x)>=0), so I assumed that they wanted me to find the volume... but I was wrong... (Crying)