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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
Then integral can be rewritten as
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
0 xe x dx lim e x x b lim
b e b b 1 |b
1 1 b1
(applying L’Hop. to limit of the quotient or just noting that exponential function dominates
the polynomial function in the numerator.)
b So the integral is convergent 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.
- Spring '10