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Unformatted text preview: ﬁwﬂwﬁ 1. (10 pts.) Find a numerical approximation to the value of 3 1
Llﬂzdx l——l———l——+——l 3 5
l ’1' 2. ,1. 3 using the Trapezoidal rule with n = 4 trapezoids. 53 u a." g (31) Um 2_£(3,;)+1}(1~)+ z Hé)+ H38
, l‘l'xa' l :. ﬁfCi)*Z(lj(g)‘)*z<r+ 2">+ 2 2. (12 pts.) Give the exact numerical value of
50
2 (3n2  7n + 2)
n=1 (Hint: Don’t forget the formulas on the cover sheet of this exam.) {a {a 70 = 3 Z In — 7 Z» + Z2
ha! In" “:1 ,6 2. 3. (48 pts.) Evaluate the following integrals: £25, a. 1+3 n”: Au: 7:1 c/x
.277
a} ~A“ '——¢Iu— ‘L Arc 4. (15 pts.) Some more integrals 2 x3+7x '2 4x2 +1
not going to help you here. a. Evaluate J dx (explain your reasoning). Hint: usubstitution is 3 .
J((70: k +7”: 1': 4K aH (Cuth
‘HCZH CCe #(’7r)=gt(x)) )9 day [KW
o; A: OV‘V' ﬂab q a)?“ b. [2 x dx=%j:?u“2du for what values of? and '2? 0 \/1+2x2 (explain your reasoning) Luz/+7.73 , brig; file. /.s’\' M15741 4L” Zwé (nJ‘7‘wC 77 X
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N 5. (15 pts.) Determine the area bounded between the graphs of y1=x2+2x+1 and y2 =2x+5 xv)"; (KlUL r” [71"77— X7} 2104 =1xc4';
'xm— ‘* = ’9
(xxt) (acV 7‘0 {a I 2. SAWS» Mr: 2.
3 @105)  («tux/r!) Jr
"2....
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 Fall '06
 JOHNSON
 Calculus

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