What is the charge on a circular disc with a varying charge density?

[technicolour1]

Homework Statement

Find the total charge on a circular disc of radius ρ = a if the charge density is given by
ρs = ρs0 (e^−ρ) sin2 φ C/m2 where ρs0 is a constant.
Are the two limits of integration from 0 -> a for ρ and 0->2∏ for φ? In the example given in the notes, ρ varies, instead of being a constant value. Does this mean that I cannot integrate ρ in this problem?

Homework Equations

Q = ∫ρdS

The Attempt at a Solution

Q = ∫∫ρs0 (e^−ρ) sin^2 (φ) dφdρ...

 

[Spinnor]

With the sin term it looks like there is as much positive as negative?

Edit, now I see the sin^2

Your integral looks doable.

 

[Spinnor]

Using as input,

integrate exp(-r)sin(phi)*sin(phi)

Wolfram Alpha gives as output,

http://www.wolframalpha.com/input/?i=integrate+exp(-r)sin(phi)*sin(phi)&cdf=1