Sketch the region enclosed by 2y=5sqrtx, y=5 and 2y+3x=8. Decide whether to integrate with respect to x or y, and then find the area of the region

Answer 1

I'd use horizontal strips to avoid having to switch curves. That makes the area
∫[5/2,5] (4/25 y^2 - (8-2y)/3) dy

Of course, you could use vertical strips, but it's more work
∫[0,1] (5 - (8-3x)/2) dx + ∫[1,4] (5 - 5/2 √x) dx

check to make sure I got the intersections right.