quiz13-10.40-soln. - ln x ± 2 dx & lim b ² ² & e...

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MATH 101-B Fall 2004 Quiz 13 (10:40-12:30 Group) January 07, 2005 Time: 20 minutes Name: Student No: Follow the directions. No work No credit!! Problem 1 (5 pts.) 1 1 ± 9 x 2 dx ? Solution. 1 1 ± 9 x 2 dx 1 1 ± 3 x ± 2 dx Let u 3 x . Then du 3 dx . Hence the new integral is 1 3 1 1 ± u 2 du 1 3 arcsin u ± C 1 3 arcsin 3 x ± ± C (switching back to the original variable) Problem 2 (5 pts.) Determine if the following integral converges or diverges. If convergent, find its value. e ² 1 x ln x ± 2 dx Solution. By definition this integral is equal to e ² 1 x
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Unformatted text preview: ln x ± 2 dx & lim b ² ² & e b 1 x & ln x ± 2 dx . Let’s first find an antiderivative to 1 x & ln x ± 2 . For this, let u & ln x . Then du & 1 x dx and we have & e b 1 x & ln x ± 2 dx & & 1 ln b 1 u 2 du & & 1 ln b u ± 2 du & ± 1 u 1 ln b & ± 1 ln b ± & ± 1 ± . So, lim b ² ² & e b 1 x & ln x ± 2 dx & lim b ² ² 1 ± 1 ln b & 1. Hence the given integral converges and its value is 1....
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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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