Mathematics 106 Final Exam: Integrals, Series, and Differential Equations, Exams of Calculus

Download Mathematics 106 Final Exam: Integrals, Series, and Differential Equations and more Exams Calculus in PDF only on Docsity! Name: ___________________________ Mathematics 106 Final Exam December 13, 2002 Problem Possible Actual 1 14 2 12 3 10 4 12 5 10 6 10 7 10 8 8 9 14 Total 100 You must show all work to receive credit. Give exact answers (ln 5, e2) unless requested otherwise. No calculators are permitted. 1. Evaluate each of the following. a) ∫ dxxx )5sin(3 b) ∫ ∞ − 0 2 7 dxxe x c) ∫ dxxx )cos( 47 2. A trough 10 feet long and 4 feet high has two vertical trapezoidal ends, each with a base width of 2 feet and a top width of 4 feet. It is filled to a height of 3 feet with water, which weighs 62.4 pounds per cubic foot. Write (but do not evaluate) an integral equal to a) the volume of water in the container b) the fluid force exerted by the water on one of the vertical ends of the container c) the work done to pump all the water over the top edge of the container