English: This uses the physics convention, where ${\displaystyle \theta }$ is measured from the "north pole". With this convention, the integral over the area can be expressed as the sphere can be expressed as${\displaystyle \int dA=r^{2}\int _{0}^{2\pi }d\phi \int _{0}^{\pi }d\theta \sin \theta }$ ${\displaystyle =r^{2}\int _{0}^{2\pi }d\phi \int _{-1}^{1}du,}$ where ${\displaystyle u=\cos \theta }$. Here, we set ${\displaystyle \phi =0}$ to coincide with the prime meridian.