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=5x^(1/2) , y=4 and 2y+1x=6

I've been trying this problem for about 3 hours.
Please help!!!!!

Answer 1

The region of interest is a triangle-ish area. The intersections are
(-2,4) (64/25,4) (1,5/2)

wrt x, divide region into two parts:

∫[-2,1] 4 - (6-x)/2 dx
+ ∫[1,64/25] 4 - 5/2 √x dx
= 9/4 + 27/25 = 333/100

wrt y,

∫[5/2,4] 4/25 y^2 - (6-2y) dy
= 333/100

Answer 2

Thank you so much!!!!!

Answer 3

no sweat. Hang in there and after a few hundred more of these, they'll be a piece of cake!