Optional Final Exam Problems

Optional Final Exam Problems--Due No Later Than 11:05am April 30

1. Find the volume of the solid formed by revolving the region bounded by the graphs of the functions given below about the x-axis. Show the integral you used. You may use technology to evaluate the integral.

2. Approximate accurate to two places to the right of the decimal the length of the given curve over the given interval. Show the integral you used. You may use technology to approximate the integral.

3. Find the area of the region bounded by the graphs of the equations given below. Show the integral you used. You must show all steps in applying a technique of integration to evaluate the integral.

4. Show the application of a test for convergence to prove that the given infinite series converges absolutely. Approximate the sum of the series with an error less than 0.000001.

5. Work Pumping Water

The water in a large horse watering trough weighs 62.4 pounds per cubic foot. The ends of the trough are isosceles triangles with a base of length 10 feet, equal length sides 13 feet, height 12 feet, with the base up as shown in the picture. The trough is 30 feet long and held in an upright position by supports on the sides. The trough is completely filled with water. How much work is done in pumping the water over the edge of the trough to completely empty it?

6. Find the center of mass of a planar lamina whose density is 2 units/square unit and whose boundaries are formed by the graphs of the functions given below.

7. Find the area and approximate the perimeter of one petal of the region bounded by the graph at the right, function given below.

Click on the picture to enlarge.

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu