Solve Surface Integral: r^2 sin(theta)

[skanda9051]

Please some one help me how to solve this problem
integral-r^2 sin(theta) d(theta) d(phi)

 

[I like Serena]

Hi skanda9051!

What did you try?
That would help me to know what I should explain to you.

 

[skanda9051]

Well its magnetic flux E through a sphere of radius r and flux is given.
integral E. da=integral 1/4pi Eo (q/r^2).(r^2 sin(theta) d(theta) d(phi) they have given answer as q/Eo:-). My doubt is since it is surface integral there should be 2 limits one with respect to theta and another with respect to phi:-). So how did they integrate with respect to phi

 

[I like Serena]

Yes, there are limits wrt theta and another wrt to phi.
This is be a double integral and not a single integral.
The limits are defined by the definition of spherical coordinates, although you do not need them to integrate your expression.

How would you integrate \int 5 d\phi?
And how would you integrate \int 5 \sin(\theta) d\theta?

Btw, in (these) spherical coordinates phi runs from 0 to 2pi, and theta runs from 0 to pi.