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 solve without having 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?
Well, yes, I know that. But what I am trying to do is trying to solve it assuming I don't know the Fundamental Theorem of Calculus (which I do, but this is just a curiosity).
Is there a way to solve this without just saying, "Oh, by definition, it's the area of a quarter of a circle, and thus it is (pi*r^2)/4"?