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math117_assignment10

# math117_assignment10 - -~:~-~ M ath 1 17 A ssignment 1 0 D...

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------ ... -~--:~--~ Math 117 Assignment 10 Fall 2008 Due November 27th or 28th 1. Adams p. 336 # 5, 7, 9, 13, 29 Suggested problems: all of Adams p. 336 2. Compute the following integrals: dx b) J c) 3 d) r a) J x2 _ 4x + 5 J x 2X3 -1 x 2 x 2 +x + 3 Jo J3 + 2x - 2 x 2 2 ± a 2 3. For integrals that contain terms such as J a - or . .; x , trigonometric substi- tutions are helpful. These substitutions make use of the identities sin 2 () + cos 2 () = 1 and tan 2 () + 1 = sec 2 e. So, for terms like J a 2 - X2, we use the substitution x = a sin (), making use of the first identity. The second identity is useful when we have terms like J ~2 + a 2 , where we use the substitution x = a tan (), and for terms of the form V x 2 - a 2 , where we substitute x = a sec Use trigonometric substitutions to compute the following integrals:
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