quiz13-8.40-soln. - MATH 101-B Fall 2004 Quiz 13...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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. ...
View Full Document

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.

Ask a homework question - tutors are online