Determining limits for a closed integration.

Question

I want to integrate a function over a closed circle in the following region. $$\oint f(x) dx + f(y)dy$$ $$^2 + ^2 ≤ 1$$ $$ ≥ $$ $$ ≥ 0$$

How do I determine the limits for the integration? I know that the first equation is a unit circle.

Answer 1

Answer to the first version of the question:

You have the limits $y=x$ and $x^2 + y^2 = 1$ which gives you $x=y= \frac12 \sqrt 2$ as the integration limit. So you integrate

$$ \int_{x=0}^{\frac12 \sqrt 2}dx \int_{y=x}^{\sqrt{1 - x^2}}dy f(x,y) $$