Change of varibles in integrals (More than 1 question)

[athrun200]

Homework Statement

Homework Equations

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.

 

[athrun200]

Homework Statement

I have questions on d and e

Homework Equations

The Attempt at a Solution

I don't know how to integrate these functions

 

[SammyS]

...
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.

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

 

[SammyS]

Homework Statement

I have questions on d and e

I don't know how to integrate these functions

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 ?