PracticeTest2 - 4) Use a trigonometric substitution to...

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Practice Test #2 – MAC2312 Directions: Use this practice test as a guide for your study for Test #2. This exam is not comprehensive, so study your quiz, class notes and homework problems in addition to completing this exam. Solutions are posted on the course website under “Solutions”. 1) Use one of Wallis’s Formulas to evaluate 2 0 10 ) ( cos dx x . 2) Find the indefinite integral for each by whichever method is appropriate. a) dx x x ) cos( 4 4 ) ( sin 2 3 b) 2 4 32 5 x x dx c) dx x x ) ( sin ) ( cos 11 3 d) dx x x ) ( sec ) ( tan 4 3 3) Use Integration by Parts to evaluate dx x x 2 6 ) ln( . Do not use a table for your calculation.
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Unformatted text preview: 4) Use a trigonometric substitution to evaluate dx x x 2 2 4 5 . Make sure to draw the appropriate triangle, label the triangle, and use it to back-substitute for x. 5) Use a trigonometric substitution to evaluate dx x x 2 5 2 2 4 9 8 . Make sure to draw the appropriate triangle, label the triangle, and use it to back-substitute for x. 6) Evaluate dx x x x x 4 20 10 4 3 2 by using a partial fraction decomposition of the integrand....
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