Area of a Plane Region

Question

Consider the region bounded by the curves y = √x, x = 4 and the x − axis. Set up

the integrals that will give the area of the region and then solve it using:

1. vertical strips

2. horizontal strips

Answer 1

2 vertical strips gives 2 + 2sqr3 = about 5.46

that's 2 rectangles: 2x1 and 2xsqr3

2 horizontal strips gives exactly 7/4 + 15/4 = 5.5

that's from 2 rectangles 7/4 x 1 and 15/4 x 1

using midpoints

the exact area = 16/3 = 5.33...

vertical strips are closer to the exact solution

use more strips to get closer

integral of sqrx dx = (2/3)x^3/2 evaluated at x=4 = 16/3

Answer 2

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