Double integral in polar form: how do you find the boundaries?

[winbacker]

Hi I need to use a double integral to find the area of the region bounded by:

r = 3 + 3sinQ where Q = theta.

I know the bounds of the inner integral are from 0 to 3 + 3sinQ.

However, I do not know how to determine the bounds of the outer integral.

Any help would be greatly appreciated.

 

[Wretchosoft]

The outer integral is just a typical single-variable polar integral. Play with the equation to figure out when the behavior of r begins to repeat itself as theta varies, paying particular attention to the periodic nature of sine. Perhaps a polar graph might help.

 

[winbacker]

Ok, well I know that once theta = 2pi, the behavior of of sinQ will repeat itself. Should I then plug in 2pi to the equation and work with that?

I know the value of sinQ becomes zero again at pi. Does this mean the outer boundary is from 0 to pi?

 

[Mark44]

0 to pi, although you can exploit the symmetry of the figure by doubling the value you get integrating from 0 to pi/2.