The force per unit area acting on a sphere with radius $r$ is $F=r^2\vec r+cos\theta \vec \theta$, what is the net force on of the sphere?
To solve this problem, i will use the surface integral and convert the force field in terms of standard basis in cartesian coordinate and do the surface integral but doing in this way completely ignored the meaning of spherical coordinates.
My question is how to do the surface integral computating with the spherical coordinate instead of converting to the standard cartesian coordinate.