# Integrating across circular surface

Niles

## Homework Statement

Hi

I am looking at a circle in a Cartesian coordinate system $(x, y, z)$, with center at the point $(0, 0, L)$ and radius R (so the z-axis is normal to the surface of the circle). From the origin (0, 0, 0), I would like to integrate across the circular surface, i.e.
$$\int_{0}^{\arctan(R/z_0)}{d\theta}\int_{0}^{2\pi}{d\phi}$$

If I instead of integrating from a point at the origin now integrate from a circle with radius R'<R (also normal to the z-axis), how would the above integrals be generalized?