Question

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y = 4√x and y = 5 and 2y+2x = 6.

Answer 1

I would integrate along dy, since the boundary changes at x=1

That makes the integral easy:

∫[2,5] (y^2/4 - (3-y)) dy

If we integrate along dx, then we need
∫[-2,1] 5-(3-x) dx + ∫[1,25/4] 5-2√x dx