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**Unformatted text preview: **November 19, 2004 Math 241 Exam 3 You must show all work.
No credit Will be given for correct answers if the work is missing or incorrect. .A 1! ﬁ‘“ N r - L m, ' 1. Set up t7. . .,.iteg.rai is; the work done by the force FOE, y, z) = a: i + myj + xyz k on a
/ particle that moves along the line segment from (0,1,4) to (1,0,4). 2. Set up the integral for the mass of the object that lies between the circles
(a: — 1)2 + y2 = 1 and x2 + y2 = 4 in the ﬁrst and fourth quadrants (:1: Z 0) if the
’ density is proportional to the distance to the origin. 3. Set up the integral for the surface area of the part of the sphere x2 + y2 + 22 = 4 that
/3 lies above the my plane and inside the cylinder 1:2 + y2 = 4y. 4. Set up the integral for the volume of the region bounded by the paraboloid V x = z2 + 2y2 and thecylinder a: = 4 — 22. 1 «1:7 ‘/—“2_12_y2
5. Consider / f / (cc2 + y2 + 22) dz dy dos.
-1 o 1 ’— (a) Convert to cylindrical coordinates but do not evaluate. (b) Convert to spherical coordinates but do not evaluate. 6. Evaluate // e(z‘y)2dA
R
3 Where R is the region bounded by the lines y = -2- ac, y = 2:13, and y = :c + 1 by using the change of variables :1: = u + v and y = u + 21). MAM 8A.“. (9 3?: yi —* x95 +xb9k
(o, I, v) we (1,0, av) irH—W 1—” (!~63< 0,1,w7 + {-dlm, «(E ‘ = <0,»-+,u4w+>« (Ma—~40
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i A) a 7 8+ 12+ 4-
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: X2 y?+bz_t(b+4 :k( Q 01-35" 3 v gge 6M b=§x bﬁ2x 51w! x .: M‘vv Lo :L4-+2V f z ‘31 % (“om v-u- 2v) 64% DH 2v ‘3 9" (WW) e M42Uiéu+grv ' 3 ; ‘Qv: fwé’iv
7. » :1- g g 2V a“ W. W ’ V“"- S g ed AAAV “:2V : 2(““"’\ o O M zV~2H“‘ZV -M2'U I 01 .L “:0 ;: Sm OQV M‘V I A“:Zwtv Rd'av: b‘Mv-ﬂ E M ;: ilk 1, " r )1, kw «1!, \ 39" )V‘ 12, , 22 , % V“ W I Qa? :: I ...

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- Math, Trigraph, Coordinate system, Polar coordinate system, dz dy dos, Sm OQV M‘V