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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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~47: ’- 4x 0 7.
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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 Hear-1H: Hath [Ir-aw 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 y-axis. 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