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Unformatted text preview: l Sarnple Exam ~ Test Four (5.1 — 5.6) You must show all of your work to receive ﬁill credit. The calculus work must be shown.
You may use your calculators simply as an aid. Evaluate each of the following integrals.
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1. “9—5le —2x)dx — SQ’I;_ 9" l) M 5
9 7"" Ll x/z +C. x __ _._ "1" .5 2. sec(3x) tan(3x)dx _:_ gee C3”) + C ‘_________.
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. \ '
1 : —’Q“\Rx'”5i +C
3. [2.76"de ‘9 7. Itanxdx : .—.Q.nlC’3k] +C eﬁxdx L“: buﬂﬂn : X‘ "'
1.
7c ¢= e. +C
2..
(.7‘ = ‘3 +C. x H.
2 UCQJx):
aﬁﬁ x 1 2. \ +C  ,3 _ — __ ____._— ”I?“ '3“ 0‘42"? 21" u—"‘"_—__ 14. Findthesum :(i2+3) ¢ LtCJXq) 4. I300: 3° + ‘1' E
i=1 (a 15. Use a(t) = —32 feet per second squared as the acceleration due to gravity. A ball is
thrown vertically upward from the ground with an initial velocity of 56 feet per second. 3. Write the position ﬁmction, s(t) and the velocity ﬁmction v(t). GH')‘: ~39 3‘73“ SCD)=O VCOD=SG
VCH: 3139M =—g2¢ +c. SLt3=SG32t +5L)olt
vLo>—;5<.=c, 30$): AWL “5"“ +C’
3C5): l(bz +5Lt *5 :0 ~19) = —3::t +59 ESLe): —H+,L «— Set b. When does the ball reach its maximum height? \IUT)‘O= —3'3t +5L=
33+=5~o 7
f: 1 59/31: AIS c. What is the maximum height of the ball?
SC 77...!) = “it(74+)z + 5b<7/'+) ‘ 16. Find the average value of f (x) = 3x2 — 2 on the interval [0, 2]. i i 7"
a _.o SQD‘1‘9)” 2 3(“3—a‘)\ o
° ... STE; _. a —L‘o—=1] I 17. If F(x)= Isin(t2)dt, ﬁnd F'(x). l F'(x 3 1 Sian") 18. Write the deﬁnite integral that represents the area of the region bounded by the
graphs of y 21+ 3/}, x = 0, x = 8, and y = 0. Do not evaluate the integral. A‘S?Q+€i7)0‘7‘ "—211!— = arcsin [E] + C
«laz—uz a I 2d“ 2 ziarctan[3]+C
a +1: or a JL=larcsec H +C
ux/uz—a2 a a ...
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 Summer '11
 MarioBorha
 Calculus

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