In the triple integral, you have functions of and as upper limits. You have to translate them into polar coordinates.
9. Use polar coordinates to compute the volume of the region defined by 4 - x^2 - y^2 less or equal to z less than or equal to 10 - 4x^2 - 4y^2.
answer in book: 6pi
my answer: 2pi
I got the root of 2 by setting the equations that bound z equal to eachother. It resulted in an equation for a circle equal to two. And to get the area of a circle, you have to do all 360 degrees, so I used 2pi. What's going wrong here?
You can translate them before you put them in the limits for Z or after you've calculated the integral for Z. But while I checked your method through with mental math, I came across my rather awful error. I basically said -4r^2 -(-r^2) = -5r^2. But it should obviously equal -3r^2.
Problem solved. No one waste any more time here!