Write double integral from D

Question

$D$ - sector in picture

I solve it and want know if it's right solution.

My solution

$D = \{-y \leq x \leq y, -1 \leq y \leq 1 \}$, so $\iint\limits_{D}f(x, y) = \int\limits_{-1}^{1}dy \int\limits_{-y}^{y}f(x, y)dx$

Answer 1

your upper bound of y is '1' but as you can see the area you want to integrate at x=0 has an upper bound somewhere between 1 and 2. You only integrate the rectangle given by the points (0.0) (-1,1) (1,1) Do you know polar coordinates ? By that your figure can easily be descirbed as a quater of a circle with radius 1 arround (0,0)