solutions2

# solutions2 - l4 Letu=ii => du= 0032 dx = c032(iu du =...

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Unformatted text preview: l4. Letu=ii => du= 0032 dx = c032 (iu) du = cos2 (u) du — + sin Eu} 1 C.‘ — 1 1 '1 sin( + C = *i’iSiDGHC 36. Letu 2:250 “5 => du = (—cse Boot d6 2:» —3du = ﬁcot ﬁesc ﬁdf) \a . : III/E _ ‘l j‘ _ ‘ _ . _ ‘ — 2 J ﬁfe/5&1! WCOIﬁLSCﬁdﬁ—J‘3d”——2”+C——2“‘3VEN—‘WNC 50. Let u = x i 4 => (in = dx and x = u + 4 . Thus 1‘03“; dx = i 4]_3xdx = fud (u + 4jdu = f(u_2 + 4u_3) du — u‘1 2LI_3:C— (x 4fI 2(x 4)_21C 60. Letu=e"":>du=e""di§I = f—cq I = f—u‘I—ELI = sec—111 + C 2 see—1 (eﬂ + C 6. (a) Letu=t2+l du tht édu tdt;t 0 u l.t J? u 8 \§ 'r a .r .r .r .r f. m? + 1>"""dt= J] du = [(3 (3) = (3W — (e) W = 56. For the sketch given. a — 1, b — 1: ﬁx} g(x} — x2 ( 2x4) — x2 + 2x4; I .3 '1 Azfxxmmx: [%+e],,:e+%)—[—%+(—%)J:%+%: 84. Limits ofintegrntion: x = 3 — y2 and x = — 3 5'2 2' 3f 3 0 30/ 2)(y+2)=0 e — 2 and d — 2; ﬂy) g(y) — (3 yg] we :» “3 182) <213>J*3(4—:g>7u_478 '14-) 115. Letu=a—x=>du=—dx;x 0 »u 3,): a »u 0 a 0 a a I _ f fo)dx _ f fLa—u) (_ du) _ f ffa—u)du _ f [La—x) dx _ o f(x)+fLa—x) _ a f(a—uJ+f(u) _ o f(u)+fLa—u) _ n f(x)+fLa—x) a El a El _ f(x)dx fLa—x)dx _ ffo——f(a—XJ _ _ a _ ,_ _ _ 2} H’ I — j; f{xJ+f(a—x] + j; f(x)+fLa—x} — j; ffo——f(a—XJ dx — 1; dx — [KID — ‘1 0 — ‘1‘ Therefore, 21 = a => I = Math 1120 Homework 2 Name: Due 9/8 or 9/9, 2011 GRADES Printoutthmpoges. Answerthe Mating-sum" in the spoon; prodded. Include full explanatimu and write Book questions / 3 your mum: in complete, mathemaﬁmﬂy and grammatically 0mm! scrum. Your amen will be meudfor style and accuracy; you will be given written Inﬁeld: on these pmb- Presentation questions / 30 Items. Wﬁteyourammtothc “bookquutiom”onupamlc paperandatoplctotlmepagu. Murillo:de for completeness. Always write neatly and legibly. Book questions -— 5.5: 14, 36, 50. 60 5.6: 63, 56, 84, 115 Presentation questions Jim I: l [10points] Evaluate dz o 1-1 .3 / "3' '1'.“ Let- x :‘AL' i‘ 'T"'.:"~ ‘ " ‘ 13— C ‘t'ﬁr km to C ‘ C“: “1" ' { Ax qi fez/L xix“ ‘r _._‘_‘_ L.1" _. a“ to ’ (‘1’ ’Ir " I-“ f - ‘ “(i it] :) EA( [(6 _ (1' aft): - .,l \..C(,' I L .n r £ (y; _ r~ .u. H (k':(_’ ) (1‘ LHf—L,‘ { _- i‘ (J r I 61‘ tr \yh— (‘56; .r «I? ( '_ - I“, u. ‘5 u? g “’1'. {'5}; 2 f I J (I t It.) r If __ d 7 J (I L )JK T f (L may“ L” Era/l l :t/ 3 _ r! t (I— I) 4‘1 r s L w’ w 3 2 ‘ - .— 4- 1“ _ '1 -*; f. _ 5 2. —: - - .. ‘H' 3L? J h 1“ 1' r- I— 1 IL __— 41.; _ _ .; tr-u‘ 1 . . CONTINUE TO THE NEXT PAGE. Alf-{WA‘LWk {'(Lc’ u— '_ k.“ ,ﬂ ' . . . . _‘:_L d. HIM" ({ l-- - - ‘J u 3h K311i I(_-_ ,1 "grin. ‘ -_’ (i: ,1- l’ , w”; I z 1. I L T -' 3‘ ﬂ '77 Math 1120, Fall 2011 Homework 2 -— due 9/8 or 9/9 2. [10 points] (5.5: 79) It looks as if we can integrate 23inxcosa: with respect to .r in three different mys: a. f2sinxcosxdz=f2udu=u2+01=sin2x+01.whereu=sinz. b. f23inxcosrdz=f~2udu= —u2+Cg= "szl'+03.Whereu=Cm1'. ain2xdx=—°"L-2’+ca. c. f2sinrmszdz=f 2 Can all three integrations be correct? Explain. fl - ~ ' u" { W‘f ‘ I. at; u.) (I in: “'“( .unq'n-I t&\ f“it'> j“ *('| 1 . Md ,_ A c X |' (J {3‘ “PA AA, “ft. (‘4‘: (a) (pm. tlggi'r éJ‘L l:\{L' r"){‘ if. 1‘. 'L A\ r{,._ (C), .— (‘13 '1‘ " I, '2(.-5‘) E) -t w. = __ _‘__..-L + (I. h a: — t v i 3 2. cu ;LL\ 1‘ {LC 5'. - — ( ‘ l r6“ r \i. L (f t. ﬁxing-l. L-‘L (-L)3""£J I: . 3 l.\'\.(t.' (C_“(Inh t f‘ _.“L a. ._(( am M ﬂ (MI E MA *‘ ) CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 2 — due 9/8 or 9/9 3 3. [10 points] (5.6: 106) Find the area of the region in the ﬁrst quadrant bounded on the left by the raids, bdow by thecurve a: = 2ﬁ. above left by the curve 1: = (y- l)’, andnboveﬁghtbythelinez=3—y. x", (1‘33) : A. ,. «kW/UH” A. 44.. Ct. 'vt": 1c r L X-l A. M“+ at“ l 3 A, Etta-4 4W=f3 ﬁlw (j: 5)—4~r;’ = “kl—é?+‘]-‘F*A,'(X‘IOX’LA) L-L Lin 5 C) “ La {CT J; ff”; MiA‘l —> “J {1-w- f» ‘- 4‘ Hut. 1 “I [1. ‘t NW? Lag I‘Lq ( ‘I ‘f 4.2:; (; ﬁfanT~-.LL.‘a "K h- (A. :5 , __ "J' w 4 w w t ..-+ at (2 a 4.; a L 1' l‘)'1.) L‘ K L F: } r“‘-"{ “k‘ '-5 I ( J'I) -'—'— Hun-g \ n ["1 t r “a '> J a) - 3— w— mm “DP u, «k 4 “‘w‘ V) - l C7 -l 4* um.( .. {A '1 L~ IL: /f‘+ i."""' {— “hit in" L'LH\‘ 9‘)" 1 r_‘ I‘LL \ k 5 1) .1 :I 50 ft" ‘*"-{ 4' (I 2) 8... (L4. 47.] - x {(.Lt‘((9[‘- Al Lnrxl (-cha I "1 r“ ‘+ 5“ L '2» M E r-E” J "% (“'\(-| {CR-f. («‘(d; (.1- f1 L L a (yr 1 'l. 1 J,(/Z"a)r(u 97"“). = LH' Li ' '2 (11-05]. "(6-6 ENE-wk "/6 ‘ IL THISISTHELASTPAGE. <0 if: {Ar,( 4.4'.‘ f] Ad Hg“ ‘4' 3 - I: J ’ "1 ' c /_I ...
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solutions2 - l4 Letu=ii => du= 0032 dx = c032(iu du =...

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