Hey everyone, this is my first thread, and I hope it will give me a good experience on this site.

Anyway, onto the question:

I have been trying to figure out a way to sum this:

Where

and

The next step is

I did some manipulating, and got:

All the help I have gotten has told me that the answer is zero, but that can't be possible, because I started with the area under the curve of the basic unit circle in the first quadrant,

and I have not made any mistakes so far.

So how can I come up with a non-zero answer for this?

EDIT:I want to solvewithouthaving to use the fundamental theorem of calculus, and just saying that it is equal to

EDIT 2:Just like for

,

is there a way I can do that sort of method the problem I have presented?