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quiz13-8.40-soln. - MATH 101-B Fall 2004 Quiz 13(8:40-10:30...

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Unformatted text preview: MATH 101-B Fall 2004 Quiz 13 (8:40-10:30 Group) January 07, 2005 Time: 20 minutes Name: Student No: Follow the directions. No work No credit!! Problem 1 (5 pts.) 1 dx ? 2x x 2 Solution. Complete 2x x 2 to a square as x 2 2x x 12 1 1 Then integral can be rewritten as 1 dx 1 x 12 x 1 2. and hence the solution is arcsin x 1 C. Problem 2 (5 pts.) Determine if the following integral converges or diverges. If convergent, find its value. 0 xe x dx Solution. By definition, this integral is 0 xe x dx b lim b 0 xe x dx . Using by parts technique, let’s find an antiderivative for xe x . We will let u e x . Then xe x dx xe x xe x e x x and v e x dx e x x 1 C C So, lim b b 0 xe x dx lim e x x b lim b e b b 1 |b 0 1 1 b1 1 1 eb (applying L’Hop. to limit of the quotient or just noting that exponential function dominates the polynomial function in the numerator.) lim b So the integral is convergent and its value is 1. ...
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