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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 7th
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'aFh HFIIH F:I'1[I llﬂlIT FUHIZ a. At what x values do the two curves intersect? KQ’~4'K 4—3 = ~73 4'7'V‘4'3 7? {LX1é‘K30
9 (2.1: (no39"!) ‘?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)’(K14K+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?
Tut15 Emu' Tr'ace Mar1H: 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 xaxis. 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 yaxis. [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 xaxis 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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 Summer '06
 JOHNSON
 Calculus, pts, thQ, ’r’i (f—~+c, FH Fsv FEv, HHD EHHET FUHII

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