Find the volume of the solid enclosed between the cylinder x2+y2=9 and planes z=1 and x+z=5
V=∫∫∫dz dy dz
The Attempt at a Solution
The problem I have here is setting the integration limits. I first tried using:
- z from 1 to 5-x
- y from √(9-x2) to -3
- x from -3 to 3
However, that gave me a negative answer, so I doubt that's the way to do it.
I then used polar coordinates for x and y and used the integral:
V=∫∫∫r dz dr dθ with limits
- z from 1 to 5-r*cos(θ)
- r from 0 to 3
- θ from 0 to 2∏
This time I got a positive answer, but I'm not sure whether the method is correct. We were never taught to use polar coordinates in volume integrals, so I'm not sure whether it's fine to mix them up.