Calculus Solutions 13

Calculus Solutions 13 - A-12 Answers to Odd-Numbered...

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A-12 Answers to Odd-Numbered Problems Section 7.3 Trigonometric Substitutions (page 299) 7~= itan-'z+?++~ tan8;$~0~~8dfI= 9 X= 5sec8;S5(sec28- l)d8= dn-5sec-I ;+C IIX=S~C~;JCOS~~~=~+C I~X=~~~~;$COSB~O=-+C -5 15 x = 3 sec 8; $ 'g"'?,dee = & + C = - dm [email protected] +c 17 x = sec8; Jsec3 8 dB = &sect9 tan8 + iln(sec8 + tan8) + C = &xdG+ ?ln(x+ dm) + C 1gX=tan8;$c~s~d~ = -L+C= -+C sina 6 sin 0 x 21 $ = -8 + C = - cos-' x + C; with C = 5 this is sin-' x = - ln(cos 8) + C = 1n 4- + C which is i ln(x2 + 1) + C 23 $ tan~~$~e 25 x = a sin 8; $:L72 a2 cos2 8 d8 = = area of semicircle 27 sin-' x]f5 = 5 - 2 = t "12 cos8d0 = -14 2 29 Like Example 6: x = sin 8 with 8 = 5 when x = oo, 8 = 5 when x = 2, Jnl3 ,h "12 3seca de = g dx = $ xn-'dx = $ 31 x = 3 tan 8; $-r12 9seca e 3]-n/2 = 33 $ xnTcln-l 35 x=sece;i(ef +e-f) = L(x+J=+ .+;=)= 2 ?(x+dZ+x--dG) =x 37 x = cosh 8; $ dB = cosh-' x + c 39 x = cosh 8; $ sinh2 8 dB = i(sinh 8 cosh 8 - 8) + C = $xd= - $ ln(x + drl) + C 41 x = tanh 8; $ = tanh-' x + C 43 (x - 2)2 + 4 45 (x - 3)2 - 9 47 (x
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This document was uploaded on 11/02/2011 for the course MAC 2311 at University of Florida.

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