tv2-1-06-ans - MAC 2312 Date: February 1, 2006 Test 1 Name...

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Unformatted text preview: MAC 2312 Date: February 1, 2006 Test 1 Name (Print) Please enclose the simplified answer in a box . Please print your name on each page. No Books. No Notes. No Calculators. Find each integral. 1. Z sin 4 x cos 5 x dx . Use the integration formula Z u 2 du = u n +1 n + 1 + C . Z sin 4 x cos 5 x dx = sin 4 x cos 4 x cos c dx = sin 4 x (cos 2 x ) 2 cos x dx Use the trig identity cos 2 x = 1 = sin 2 x . = Z sin 4 x (1- sin 2 x )cos x dx u = sin x du = cos x dx = Z u 4 (1- u 2 ) du = Z u 4 (1- 2 u 2 + u 4 ) du = Z u 4 du- 2 Z u 6 du + Z u 8 du = 1 5 u 5- 2 7 u 7 + 1 9 u 9 + C = 1 5 sin 5 x- 2 7 sin 7 x + 1 9 sin 9 x + C 2. (a) Z x 3 dx √ 4- x 4 Use the integration formula Z u n du = u n +1 n + 1 . Z x 3 dx √ 4- x 4 = Z (4- x 4 )- 1 2 x 3 dx u = 4- x 4 du =- 4 x 3 dx =- 1 4 Z (4- x 4 )- 1 2 4 x 3 dx =- 1 4 · 2 (4- x 4 ) 1 2 =- 1 2 (4- x 4 ) 1 2 + C (b) Z x dx √ 4- x 4 Use the integration formula Z du √ a 2- u 2 = arcsin u a + C Z x dx √ 4- x 4 = Z x dx q 2 2- ( x 2 ) 2 u = x 2 du = 2...
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This note was uploaded on 02/21/2010 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.

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tv2-1-06-ans - MAC 2312 Date: February 1, 2006 Test 1 Name...

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