Find the arc length of the curve below on the given interval by integrating with respect to x. y=2x^(3/2); [0, 1]

The arc length of over [0, 1] is given by the integral,

Differentiate y with respect to x using the power rule:

Then the integral becomes

Substitute u = 1 + 9x and du = 9 dx :

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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