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Unformatted text preview: Midterm 2 Practice Warning: The problems below are meant to help you prepare for the first midterm. Doing these problems is a good thing to do. However the questions that will appear on the test may vary in type or style from the ones below. Doing nothing more than these problems is a bad thing to do. 1. Use integration by parts to evaluate the following integrals: (a) R x cos( x ) dx ; (b) R x 2 sin( x ) dx ; (c) R ln( x ) dx ; (d) R 4 1 x ln( x ) dx ; (e) R sin(ln( x )) dx . 2. Use partial fractions to evaluate the following integrals: (a) R 1 ( x +4)( x- 1) dx ; (b) R 1 x 2- 9 dx ; (c) R 5 x +1 ( x- 3) 2 dx ; (d) R x 3 +1 x 2 +2 dx . (e) R 3 2 1 1- x 2 dx . 3. Determine whether or not the following improper integrals converge or diverge and, in the case of convergence, determine its value: (a) R e 1 x (ln( x )) 3 ; (b) R - xe- x 2 dx ; (c) R- sin( x ) dx ; (d) R 1- 1 ln | x | dx ....
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This note was uploaded on 02/22/2010 for the course MATH Math 4B taught by Professor Alla during the Spring '10 term at UCLA.
- Spring '10