I need to compute the vector field which is given in spherical coordinates. As the unit vectors are dependent on the position I cannot integrate it right off the bat. I have
$$T(\theta,\phi)(\hat{\theta}+\hat{\phi}) sin(\theta)d\theta d\phi$$ for $0<\theta<\pi$ and $0<\phi<2\pi$.
Do I just replace the unit vectors with their corresponding cartesian coordinate unit vectors and integrate?