------...-~--:~--~ 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) Jx2 _ 4x + 5 Jx 2X3 -1 x2x2 +x + 3 Jo J3 + 2x -2 x2 2± a23. For integrals that contain terms such as Ja-or ..;x, trigonometric substi-tutions are helpful. These substitutions make use of the identities sin2 () + cos2 () = 1 and tan2 () + 1 = sec2 e. So, for terms like Ja2 -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 + a2, where we use the substitution x = a tan (), and for terms of the form Vx2 -a2 , where we substitute x = a sec Use trigonometric substitutions to compute the following integrals:
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