Solutions to Exam 3 (Blue Version) Ma123, F05

# Calculus (With Analytic Geometry)(8th edition)

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Unformatted text preview: 30me; P EWM “DI - BLUE 1. (46 pts.) Compute each of the following integrals: _ I _|‘_ V a.IxJ;2dx 1: S '(Clz‘ "2-" I An ': LL rL LL + C (2/39 ((6’) [E bj t2+2 “=- 421*?- 40.1 7-th la 7" u is“: re continued next page 0‘: "we 'ﬁ ’K: I—oL Juz—JX 2J1— dx x x _Clu= 4x I o S XtdFX c‘K : __ (ka'faclu o l o o 31 5 :1’8 (I'1“*'“L)“lltc‘u :_\$ “k—lu/ +u/1 Ju l t 3/1, 51 1/,_ D :~ (A ~fo_4—._‘ﬁ_ /AO-~<E_1 (3/1) (7/74 ( h) ' 3 5 2 +3. q 3 5 7 %é\ -lclu w 7‘ ‘L I’VX'L r Au': '1xéx / *iéu: ‘xéuc 9C 3 ﬁalx : PL J. .ALL (’XL) L a? -2 :-l—Su—3AU‘~ ’r’i (f—~+c 2— —--2. ; i 2. (18 pts.) Consider the two curves f(X)=x2—4x+3 H17“; , g(x) = —x2 +2x+3 shown below: sz 21mm Truce Fmﬁlr'aF-h HFIIH F:I'1[I l-lﬂlIT FUHIZ a. At what x values do the two curves intersect? KQ’~4'K 4—3 = ~73 4'7'V‘4'3 7? {LX1-é‘K30 9 (2.1: (no-39"!) ‘?C=- 0/3 b. Write a single integral (don’t evaluate it) for the (shaded) area between the two curves. ,7: ~KL+21<+3 ’3 g ;(C,— 7(14- 11k3)’(K1-4K+33> 47C 0 v ’3 c 762'*4'1<*5 A 7‘ 3. (13 pts.) Determine the following: d x -4 p- ; _l"t +1dt “Ker £1 : 2 a x1 1 ’5 4. (19 pts.) The region between the curve (597" f 2 g ,_ 7C1. \$ ’ a. __ _ 2 y—ZJZS x K1 2 2;, ’7/+ and the x—axis in the first quadrant is shown below. Note that (5,0) and (0,10) are points on the curve. 1. 'X 2 25" 7 /4‘ Fiv sz F3 FH Fsv FEv F? Tut-15 Emu-'- Tr'ac-e Mar-1H: Hath Draw Pen ':| < D! ‘0 7 ' | / (5 a) h x. HFIIH m EHHIZT FUHE a. Write, but don’t evaluate, an integral for the volume of the object obtained when revolving this (shaded) region about the x-axis. 5 I (r 61 WfA'K O b. Write, but don’t evaluate, an integral for the volume of the object obtained when revolving this (shaded) region about the y-axis. [0 K?0 7C: 47- J 2;,,71/+) 47 25’ ‘7"/<I~ D Hint: The answers to parts a. and b. are different. 5. (9 pts.) The region below the curve f(x)=x3 +3x2, 15x32 and above the x—axis, for 15 x S 2, is displayed below: HHIH HHD EHHET FUHII Which of the following is thq upper sum ylpproxima’ting the area under the curve and above the x-axis between 1 and c oose one)? } "-11 i 3 i 2 ii. Z—Kn—J +3(1+—) ] / i=0" n n " 1 i 3 i 2 111. —- 1+— +3 1+— ,-=on n n ,.:¢[(2)’+3(2ﬂ for ﬁ WW ...
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