/sci/ - Science & Math

Still working on getting an agreeable answer here that I understand. My work thus far is
[math] \int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\int_0^{\frac{\pi}{4}}
2sin(\phi)cos(\theta) + 2sin(\phi)sin(\theta) + 2cos(\phi) [4sin(\phi)]d\theta d\phi
[/math]

Does that look right? As long is the integration is set up correctly I can handle the remainder ezpz. One of the anons who helped me in the last thread said the [math]p=2 \rightarrow p^2 = 4[/math], so that's why I have 4 in the square brackets, but I was wondering how p was determined so easily, is it as easy as just finding the max value out of the <i,j,k> components in my function? Probably, just wondering though. I feel somewhat confident in the form of this answer so I'm gonna proceed but lmk if it looks wrong pls

is this as easy as setting a double integral in terms of theta and phi? like
[math]\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\int_0^{\frac{\pi}{4}} ()d\theta d\phi[/math]

where the middle is just the given vector equation?