Homework Help: Change of varibles in integrals (More than 1 question)

1. Jul 17, 2011

athrun200

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Why I can't integrate$\theta$ from 0 to 2$\pi?$ Then integrate $\varphi$ from 0 to $\pi$. It seems it can also generate a sphere.

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2. Jul 17, 2011

athrun200

1. The problem statement, all variables and given/known data
I have questions on d and e

2. Relevant equations

3. The attempt at a solution
I don't know how to integrate these functions

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3. Jul 18, 2011

SammyS

Staff Emeritus
For 0 < θ < π sin θ is positive, for π < θ < 2π sin θ is negative.

4. Jul 18, 2011

SammyS

Staff Emeritus
For (d) : You have the wrong limits for the θ integration.

Also, the density is given by ρ = M π a2, where M is the mass of the circular lamina and assumes that ρ is the mass per unit area.

For (e): Your integral has both r & θ in it.

I suggest using r = 2a cos (θ) to find dr/dθ . What are the limits of θ for this integral ?

Last edited: Jul 18, 2011