Find the area described by $S=\{(x,y)\mid -2<x\leq 0, 0\leq y\leq 2/\sqrt{x+2}\}$

Question

Find the area described by $S=\{(x,y)\mid -2<x\leq 0, 0\leq y\leq 2/\sqrt{x+2}\}$.

I have tried to use logic to figure out what to do but cannot figure it out. I have tried to think about this region as a set of values that satisfy the conditions but then I have no idea how to integrate it if that is the case. Thank you.

Answer 1

$\int_{-2}^0 \dfrac{2}{\sqrt{x+2}} dx =4\sqrt{x+2}\quad|_{-2}^0=4\sqrt{2}$