Calculus
posted by Donna on .
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^(1/2)), y=4, and 2y +2x = 6
I keep getting an area around 21.3 but it is incorrect. Am I close?
Thank you!

odd that one function is written as
2y = 4√x
why not just y = 2√x ?
Anyway, assuming the functions are correctly written, the area is roughly triangular, with vertices at (1,4),(1,2),(4,4)
Integrating along x, we need to divide it up into two regions, over [1,1] and [1,4]
a = ∫[1,1] 4  (3x) dx + ∫[1,4] 4  2√x dx
= (x + 1/2 x^2)[1,1] + (4x  4/3 x^(3/2))[1,4]
= 2 + 8/3
= 14/3
Integrating along y is easier, since we just subtract the left from the right:
a = ∫[2,4] y^2/4  (3y) dy
= y^3/12 + y^2/2  3y [2,4]
= 14/3