Homework 5Solutions

Exercise 1. A particle is moved along the x-axis by a force that measures 10/(1 + x)2

pounds at a point x feet from the origin. Find the work done in moving the particle fromthe origin to a distance of 9 feet.

Exercise 2. A circular swimming pool has a diameter of 24 ft, the sides are 5 ft high,and the depth of the water is 4 ft. How much work is required to pump all of the waterout over the side? (Use the fact that water weighs 62.5 lb/ft3.)

Exercise 3. Sketch the region bounded by the given curves and find its center of mass.

1. y =√x, y = x

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2. y = x+ 2, y = x2

3. y = sinx, y = cosx, x = 0, , x = π/4

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Exercise 4. Find the length of the curve

1. y = 1 + 6x3/2, 0 ≤ x ≤ 1

2. y = ln(cosx), 0 ≤ x ≤ π/3

3. x = 13

√y(y − 3), 1 ≤ y ≤ 9

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