Find the region for double integrals

Question

I have the integral $I = \iint_D\frac 1 {\sqrt x} \, dx \, dy$, where $D: y^2 \leq 8x, y\leq 2x, y+4x\leq 24$. I don't know how to find the bounds for this regions. In general what is the way to find these bounds?

Answer 1

In the general case, to find the boundaries of y, find the lowest function as a lower bound and the largest is an upper bound. As for x, the leftmost function is the lower bound and the rightmost one is the upper bound.

Answer 2

Your region looks something like this.

You will need to break this region up to integrate it.