# Calculus

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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!

• Calculus -

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 - (3-x) 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 - (3-y) dy
= y^3/12 + y^2/2 - 3y [2,4]
= 14/3

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