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Unformatted text preview: 16B CALCULUS
Francisco Santos Nov 8, 2007 Practice Midterm 2 Name: rev" as” ID: 1. (3 points each, 24 in total) Evaluate the following indeﬁnite integrals. Simplify your answers
as much as possible. Show your work. You may use u—substitution, trig formulas, the
simple power rule, the fundamental theorem of calculus, integration by parts, partial
fraction decomposition, etc. '1 Zx—E . .4
a f($+1)ex2+2“_5dx= T:— jCZKPZ) 6" f 01 x :JCMCJZMIEI‘CM‘" C:
I .)(,1+2K ' 5)
: '7" +
zé c / . w
b. fsecloxtanxdxz/%quv($LCKVLaMK)a/KS/Aqézu: y sf: I0 ) Mrsecx i7; 7 1L
Name: Marc/0 SW05 2. (3 points each, 6 in total) Evaluate the following deﬁnite integrals. Simplify your answers as
much as possible. Show your work. You may use u—substitution7 trig formulas, the simple
power rule, the fundamental theorem of calculus, integration by parts, partial fraction decomposition, etc. z z z! _ 2/ 7.1 2
f .. .37. — _
“WM 4;) U 0 : 2/22 0 a. I: m —m>2°dx=w:gz,{/(T§gej r i
l u: x (/5 'K 19‘ Z (4)22” (07
z! l : —— — _
aim: 5L 0—544—0 j 2% Z] '22, _‘ '\_. \v’ I l /uzao[u+/u “ML” ID:_______ 3
’4 (1'33 Q a 3‘ v1 _ u
b. flxsilode/ de d”:/(1*9M+27~LZ M
o ‘4 3 t4
3 a . 3. (5 points) Find the area of the region bounded by the graphs of a: = 3312 and m = ~y2 + 4y.
Set up but DO NOT EVALUAT E the integral(s). Jammy“ E/ ML m; ‘we,
[00} Q)’ Wall—fold), (go; Name: a; co 5 M135 ID: 4 4. (10 points) The outdoor temperature at time t hours is modelled by T(t) = 40 + (552?. a. What is the initial temperature? Ho) we 9?: b. What is the temperature after ours?_ ‘ 5’0 a
ﬂow/9+ “:4 W
5 _,,___.__._.
c. At what rate is the temperature changing when t = 4 hours?
/é 7. £3. a  n, 276
T (Lu/)3 / TIM): 541)” d. What is the AY/ERAGE temperature between t = 0 and t = 4 hours? (7
’ c z E a ,
4m .M/0 m) a”: *4/6er €6,150" 5 r W ‘ m) "
y ‘f ’(9 L/ o L“ ) 9 o P4 W .29. _L »
,7ﬂ{§,.7¢0+/)ﬂ9 200 5. (5 points) Consider the enclosed region R bounded by the graphs of y = In x, x = e, y = 0.
Set up but DO NOT EVALUATE the integral(s) which give the VOLUME of the solid
of revolution formed by revolving the region R around a. the artaxis ...
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 Spring '11
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