quiz10-8.40-soln. - ) 1 )( ( 1 ) 1 )( 1 ( 2 2 1 2 2...

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MATH 101-B Fall 2004 Quiz 10 (08:40 – 10:30 Group) Dec. 17, 2004 Time : 15 minutes Name: ___________________ Student No: ___________ Follow the directions. No work = No credit!! Problem (6 + 4 pts) a. Find upper and lower bounds for dx x x e & - 2 1 2 1 Express your reasoning in words. Solution: We first find the bounds for the function inside the integral. [ ] 2 2 2 e 1, on 0 1 ) ( 1 1 ) ( < - - = - = - = - x x f x x x x x f So, the function is a decreasing function: ) ( 1 ) 1 ( 2 2 e f x x f - From comparison of integrals:
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Unformatted text preview: ) 1 )( ( 1 ) 1 )( 1 ( 2 2 1 2 2 2-≥-≥-& e e f dx x x e f e b. Evaluate the definite integral ? 1 2 1 2 =-& dx x x e Solution: We first find an antiderivative for the function in the integral, C x x dx x x dx x x +-= ± ² ³ ´ µ ¶-=-& & 2 ln 1 1 2 2 Now use this to evaluate the definite integral: 2 5 2 1 ) 1 ln( 2 ) ln( 2 ln 1 4 4 2 1 2 1 2 2 2 e e e x x dx x x e e-= +--= ± ± ² ³ ´ ´ µ ¶-=-&...
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This note was uploaded on 03/24/2012 for the course MATHEMATIC 101 taught by Professor Many during the Spring '10 term at Sabancı University.

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