I want to integrate a function over a region R, which is determined by the following conditions. $$x^2+y^2\leq1$$ and $$x+y\geq1$$
My region is determined by these two inequalities. I know that the first expression produces a unit circle, which contains all points within the unit circle, including the boundaries.The second expression is a line passing through $y=1$ and with a slope of $-1$.
The region is given to be between the unit circle and the line .I do know what the region looks like , but I do not know how to express it in terms of integration limits, so I can integrate it and find the area, or just do a general integration over this region. I tried to use polar coordinates, but still couldn't figure it out.
Can you guys help me determine the integration limits for this region ?