$(a)$ Sketch the region of integration in the integral
$\int_{y=-2}^{2} \int_{x=0}^{\sqrt{4-y^2}} x e^{{(4-x^{2})}^{3/2}} dx dy$
By changing the order of integration, or otherwise, evaluate the integral.
$(b)$ Let $R$ be the region in the $x-y$ plane defined by $0 \leq x \leq y \leq 2x$, $1 \leq x+2y \leq 4$. Evaluate: $\mathop{\int\int}_{R} \frac{1}{x} dx dy$
I understand how to draw these but I am not sure how to caluculate the limts in either case (especially part $b$).
Can someone explain how we calculate the limits for integration? Once I know that I am sure I can integrate the function myself. Thanks!!