Find area bounded by loop

I can do the integral for these problems all day long but cannot determine the boundaries to save my life. Polar coordinates are my arch nemesis at the moment.

The problem:

find the area bounded by =

1.

2. find boundaries

3. do integral

4. win

I must have been catatonic when boundaries were explained because I simply do not get how to find them.

thanks for any help!

Re: Find area bounded by loop

First, note that goes from 0, up to +1, then down to 0 again as goes from 0 to . For from to , sine is negative so you just go over the same path again. That is, covers one loop as goes from 0 to . Here, is replaced by so this function covers one loop as goes from 0 to . That is, as goes from 0/3 to .

Re: Find area bounded by loop

I follow that. Does 3 at the beginning of the function not make a difference then?

Re: Find area bounded by loop

No, that does not affect the values. In fact, it could be taken outside the integral.

Re: Find area bounded by loop

Oh, okay. So if I have a function like I only need to look at ? But this is only for multiplications of functions correct? In other words I could not pull out "n" or "k" in this example: . Do I have this right?

And, in general form I could solve by and the solution to would just be between 0 and .

Am I thinking of this correctly?