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Unformatted text preview: Math 122 Final May 1, 2009 SI: Name 1 /15 2 /15 3 /15 4 /15 5 /15 6 /15 7 /15 8 /15 9 /15 10 /15 11 /15 12 /15 13 /15 Style Points /5 Total Directions: 1. No book, notes, or letting Charles graduate. You may use a calculator to do routine arithmetic computations. You may not use your calcu lator to store notes or formulas. You may not share a calculator with anyone. 2. You should show your work, and explain how you arrived at your an swers. A correct answer with no work shown (except on problems which are completely trivial) will receive no credit. If you are not sure whether you have written enough, please ask. 3. You may not make more than one attempt at a problem. If you make several attempts, you must indicate which one you want counted, or you will be penalized. 4. You may leave as soon as you are finished, but once you leave the exam, you may not make any changes to your exam. Have a Safe and Happy Summer 1. (15 points) (a) Z 1 2 + 2 √ x dx (b) Z e 4 x (4 3 e 2 x ) 2 dx Hint: Z u ( a + bu ) 2 du = 1 b 2 a a + bu + ln  a + bu  + C (c) If f ( x ) is continuous and differentiable, f (1) = 5 and 1 Z f ( x ) dx = 3, find 1 Z x f ( x ) dx 2. (15 points) (a) Z sin 2 x cos 2 x dx . (b) Z sec 4 x dx (c) Z 1 √ x 2 + 9 dx 3. (15 points) (a) Z 1 x 2 4 x + 8 dx . (b) Z x + 4 x 2 2 x dx (c) ∞ Z e x √ 1 e x dx 4. (15 points) (a) Find the solution for the following differential equation: 2 y dy dx = x 2 + 1 cos( y 2 ) y (0) = r π 2 (b) Find the general solution for the following differential equation: e x dy dx + 2 e x y = 1 (c) Solve the following differential equation y 00 8 y + 16 y = 0 5. (15 points) An engine has 100 quarts of oil. To change the oil while the engine is running, a machine is attached that removes 5 quarts of oil each minute from the engine and replaces it with 5 quarts of new oil. Letoil....
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This note was uploaded on 02/17/2010 for the course MATH 122 taught by Professor Butler during the Spring '07 term at Case Western.
 Spring '07
 Butler
 Math

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