Use polar coordinates to set up and evaluate the double integral $$f(x, y) = x+y $$ $$ R: x^2+y^2 \leq 25$$ with $ x \geq 0 , y \geq 0 $
I know this is a circle and all. But the area they are talking about is $1/4$ of a circle. Is it a different formula from a half of a circle? I'm confused about what to do. I really need all the help I can get. Thank you!
It is actually a quarter circle not a half circle because both your x and y are positive so you are in the first quadrant.
The integral is $$\int _0^{\pi /2} \int _0^5 (r\cos (\theta)+ r\sin (\theta)) rdr d(\theta)$$