Evaluate the triple integral where is bounded by the parabolic cylinder and the planes and .
Thanks.
Make a graph of x vs y and x vs z.
The points of intersection on the x vs y graph are where 8x^2=16x (x=0,2)
So, for the x integral let x go from 0 to 2.
Now for the y integral..
On the x interval [0,2] y=8x^2 < y=16x so let y range from 8x^2 to 16x.
Now for the z integral..
It is bounded by z=0 and z=4x so let z range from 0 to 4x.
dV=dz dy dx
Now just integrate the function with respect to z, and then plug in the limiting values.
Integrate with respect to y and plug in the limiting values. Finally, integrate with respect to x from 0 to 2.
Hope that helps..