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Unformatted text preview: joLqucs  gamut a: ..
mum/e l. (18 pts.) Consider the two curves shown below: HHIH Fiﬁlil EHHET FUHC a. At what x values do the two curves intersect? 1 21¢ ( 7c ~37 " o b. Write a single integral (don’t evaluate it) for the (shaded) ween the two curves. 2. (13 pts.) Determine the following: d x .
a _l t(s1nt) dt = (53.x) 3. (9 pts.) The region below the curve
f(x)=x3 +3x2, ISxSZ and above the x—axis, for IS x S 2, is displayed below: HFIIH FiFIIII EHFIIIT FUHE
Which of the following is approximating the area under the curve and
above the x—axis between 1 .  oose one)? ; iii. 21
 n "it3 i2
iv. ——+3—
n) t] Fur rp cleansed“?
("c Jakl. 4‘14 K6771»? mg (he! ﬂaky/3?; Q}, [444'
M’Vaiéb 4‘0 0547.; m 50% 4. (46 pts.) Compute each of the following integrals: a.IxJ';3dx 5 S “Xi/1‘" Ax: 9/2 V 'L
'X 23‘.+c 37;) (1/1,) H bjx/t—ZTS (Ast45 ‘
H“ ,L A“ JcAJr continued next page 1 ("7:1
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*~ 0“) ﬂclu r. 25" 7(2 2.
2.
5. (19 ts.) The re ion between the curve a.
P g : 2 5‘ _ 7c
y = 2" 25—x2 a.
x1 t 25 t '7 /+ and the x—axis in the first quadrant is shown below. Note that (5,0) and (0,10) are points on the curve. x : r7; 5 ‘_ 7«/$ Fiv ' sz F3 FH FEv FEv F? S!
Took zoom Trace Hear1H: Hath [Iraw Pen =2 ll ll /f°) HHIH Fiﬁlil EHFICT FUHC a. Write, but don’t evaluate, an integral for the volume of the object obtained when
revolving this (shaded) region about the yaxis. 43W 07" (J 15» MW >217 [V (Y D 7C:¢7 K;
dzf~o"‘/+ b. Write, but don’t evaluate, an integral for the volume of the object obtained when revolving this (shaded) region about the x—axis.
’7 2 ‘2_ m; ( 5W(zfz;::>147‘
a Hint: The answers to parts a. and b. are different. ...
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 Summer '06
 JOHNSON
 Calculus

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