Final answer:
When evaluating an integral in cylindrical coordinates, we use the variables (r, θ, z) instead of (x, y, z). To express the answers in a coordinate system that has the origin at the center of the cylinder, we use polar coordinates (r, θ, z) and set the origin at the center of the cylinder.
Step-by-step explanation:
Integral Evaluation by Cylindrical Coordinates
When evaluating an integral in cylindrical coordinates, we use the variables (r, θ, z) instead of (x, y, z). Here's how the coordinates relate to each other:
- x = r cos(θ)
- y = r sin(θ)
- z = z
To express the answers in a coordinate system that has the origin at the center of the cylinder, we use polar coordinates (r, θ, z) and set the origin at the center of the cylinder.