kelly070280
New member
- Joined
- Jul 7, 2006
- Messages
- 7
Use cylindrical coordinates to write a triple integral that gives the volume bounded below by the cone z = √(x² + y²) and bounded above by the plane z = 2.
With cylindrical coordinates, x² + y² = r². So if z = √(x² + y²), then z = r because it would be the square root of r² which would be r.
The integral I wrote would be:
triple integral {z=2 to r, r=1 to 0, theta = 2pi to 0} r dz dr dtheta
I know how to evaluate it, but I wasn't sure if I put the z values in the correct order. Should it go from 2 to r, or from r to 2?
Thank you!
With cylindrical coordinates, x² + y² = r². So if z = √(x² + y²), then z = r because it would be the square root of r² which would be r.
The integral I wrote would be:
triple integral {z=2 to r, r=1 to 0, theta = 2pi to 0} r dz dr dtheta
I know how to evaluate it, but I wasn't sure if I put the z values in the correct order. Should it go from 2 to r, or from r to 2?
Thank you!