So it looks as though the first integral should be .
The hardest part of the question is probably to figure out the region over which you are supposed to be integrating. In this case, y goes from the circle to the line , and x goes from (which is where the line crosses the circle) to x=1. Draw a picture to see that the region of integration is the bounded by the unit circle, the line y=x and the line x=1. You will then be able to see from the picture that this region is described in terms of polar coordinates as follows: θ goes from 0 to π/4, and for each fixed value of θ, r goes from 1 to sec(θ). So the integral becomes . Once you have got that far, the actual evaluation of the integral should be easy.
Do the other questions the same way. The key step is to draw a picture of the region of integration.