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Unformatted text preview: Calculus I Exam #1
Fall 2011
Sections 6.15.6 Name Show all of your work on this paper. Solutions without appropriate supporting work will not earn credit, even if correct.
Answers should be exact unless stated otherwise in the problem itself. Only your best 10 attempts will count towards your grade. © 1. Set up the integral to find the volume of the solid generated by revolving the region bounded on the left by the
arabol 2 +1 and on the right by the line x = 5 around the yaxis. Do not evaluate the integral. hawk—l 9 S
2. Set up the integral to find the volume of the solid generated by revolving the region bounded on the left lin the
parabola x = 2 + .  ' ’ z 5 around the line x : 7. Do not evaluate the integra . e vo ume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = 2 cos x, and the line x 2 TE/ 4 about the line at = rt.
Do not evaluate the integral. l
l 1 "7:4 “77, X47“ 4. lfa force 'of 90 N stretches a spring 1 m beyond its natural length, how much work does it take to stretch the
spring 5 m beyond its natural length? Make sure you evaluate this one. Clo: RC!) 5
llth W: 50 90x Clx 5. A reservoir resting on top of a 60 ft tower is shaped like a hemisphere, base down, and has a 20 ft diameter. Set
up, but do not evaluate, the integral to find how much work it takes to fill the tank with water pumped from round level. Recall that the density of water is 62.4 lb/fta.
die a... I  " “18’
(at) W Y2+ “at: lOO 6. Find the length of the curve y = x2 — (lnx)/8 on the interval 1 S x S 2. ’ _.,J———.. Kali”;
‘3‘91 9x “"97!” :9 2. '2. — lioer ‘ :. =~ stow—32x”le
erg ,+( W) on 5' Wax
_ t 25W+32x1+l cm : 2 loos/WY (ix 8‘? . 8' X ' , a. 21
“'5: %4X 3£2(5L>L+’i"x)olx
L:1++j;'7ﬂn2rl~o 7. Find the surface area of revolution for the solid generate! hy revoivrng the portion ofthe curve y = 9 — x2 that
lies in the first quadrant about the y—axis. ! $3 2W 3dox rZﬁﬁxllwxadx 8. A rectangular tank used to catch runoff water has a height of 20 ft and base that measures 10 ft x 12 ft is
underground with its top 6 ft below ground level. Assume that the water weighs 62.4 lb/fta. r a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is b. Ifthe water is pumped to ground level with a (5/11)hp motor (work output 250 ft—lb/sec), how long will it
take to empty the full tank to the nearest minute)? l
ZBClGHaO 6*"5 m... ,._, . 40% H 9. Consider the region bounded in the first quadrant by the curves y = e" + 1, x = 1, and y = 1. Setup, but do
not evaluate the inte rai to find the volume of the solid generated by revolving the region about the yaxis. 10. Consider the region bounded in the first quadrant by the curves, y = e" + 1, x = 1, and y = 1. Set up, but do
not evaluate, the integral to find the volume of the solid generated by revolving the region about y=1. constant. .2 £3 k X ‘L 3 ‘
isoo= %>L lo 8. Given r(t) = (3 sin t)i + (3 cos t) j + 4tk (6 points each) 3. Find the unittangent vector. : +(ﬂ38fn‘e)f 1”” E ‘ WM: 1 {cm 4,me + lco :g «— , '60315 4' ‘
d. Findthetorsion. E 4( 3"” A ,> 5cm: 4% q : liméi’lzgwd’w’ I : ’asamk #Sant O ...
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 Spring '12
 PamelaSatterfield

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