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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 Lei5 ..‘ '2. z \ 7.
g\ VOL'2. SO W):(33l(3/l3}}c§3 ;21r§ggﬂ(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: (Joliex 3  1x
rJT/ V .. 5h B3.(10 points) Find the volume when the area bounded by y = sin(:c) and the :caxis 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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 Fall '08
 Bonner
 Calculus

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