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exam1A_soln - Your Name Printed Clearly Your Discussion...

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Unformatted text preview: Your Name Printed Clearly! Your Discussion Leader Name Discussion Period EXAM 1A 0 BOYLAND o CALCULUS 2 0 FALL 09 PART A: Short Answers Do not show work, just give the answer in the space provided. A1.(2% points) Write down,.but do not evaluate, the integral that gives the volume when the region bounded by y = x and y = x2 is rotated about the line a: = 3. S tells Answer: («M‘s Lei-5 ..‘ '2. z \ 7. g\ VOL-'2. SO W):(3-3l-(3-/l3}}c§3 ;21r§gg-fl(x-,jé) 3 A2.(2% points) Write down the formula using an integral that gives the average value of the function f (x) = m3 on the interval [1, 3] and then evaluate it. 3 8‘ Ni : Answer:3‘E\S‘?>X3qLY -: 4 -%;:f l ::E? ‘1‘ [O 2. a ,3. 2x * A3.(2% points)fcoszxdac= Si ( \ +605 2743A7< - Z (x + 5L“; +C A4.(2% points) What substitution would you use to integrate 2: dm? /\/9*$2 __. 2 Answer: X ‘:_ 36"4 6. OR (4 -~ 7—X TR\3 Serb SWWR Sub. Total points this page out of 10 PART B: Long Answers Show all your work and justify your steps for partial credit. B1.(10 points) Find the area of the region bounded by y = $2 — 4a: and y = 22: — 3:2. swim—2 xix—0M ‘3: arms“: x Orr.) \fl 1 L{ (L - 2 X’fo’elre—r ‘ ’2‘ ,_ o S of Qua—*é7fi— . 1* (XPj) :— 50 H‘Kvsecfi'ton 4+x: [$23 . 3 APQq Z. 274 #2 “(7 fifléx 330*é$;2)€q 4.x 0 3 z édeng 337.4828] 33 g 0 Total points this page out of 10 B2.(20 points) Compute the following integrals: 3X 3x (alfeszcoshdx : fl 5‘AD‘X -* 356 SMZX AX 5‘ ._ SQA". 13““A“ 2 LL '19 " £r+c 2 5‘59— 56/639? (4: 5&6? , 7 s 7 5‘ A“: fiecg'lfiJ’ “it? ,. Total points this page out of 20 B2.(20 points) Compute the following integrals: 3X 2 3x A 3:16 : g (a)fe cos2xda: a 5"“ X .. 256 quZX X .57; iv: (Jolie-x 3 - 1x rJT/ V .. 5h B3.(10 points) Find the volume when the area bounded by y = sin(:c) and the :c-axis for 0 3 ac 3 71' is rotated about the y—axis. (Wm/é. ) fi \MAS ( womb/vs m9 093 \ WT _. cos><\ ‘15:” NS X§I“>‘A7<:l“[x‘ o 0 TY _. W +Séo$7<<lT]'—. Total points this page out of 10 ...
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