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MTH203 SP05(Exam 3)

# MTH203 SP05(Exam 3) - American University of Sharjall...

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Unformatted text preview: American University of Sharjall Department of Computer Science, Mathematics, and Statistics MTH 203 - EXAM III Spring 2005 Name: ID# Section# Instructor Name Q1. (14%) Set up triple integral in cylindrical coordinates to evaluate the integral I” ex2+zde, where Q is the region bounded by x2 +7.2 = 4, y E 0 and y = z. (Do not evaluate the il3tegral) ' (9 9/7le (2, ZMSL @ Ming 0W“ 0L/ 2 O 0 ‘ QZ.(14%) Set up triple integral in rectangular coordinates to ﬁnd the volume of the region in the ﬁrst octant bounded above by the cylinder z = 1 —y2 and lying between the vertical planes x + y = 1 and x + y = 3 (Do Not Evaluate the integral) 03.(14%) Set up triple integral in spherical coordinates to find the volume of the solid bounded below by the sphere x2+y2+22= 22 and above by the cone z = 1/3x2+3y2 .(Do not evaluate the integral) 94‘ 2 it b V j @ WW,MM\X/~\ ﬁ/ 0 ”2/ ,9” x V” W 7 r 04. (22%)Find the work» done by the force ﬁeld F(x, y, z) = (y + z)i + (x + 2)] + (x + y)k on a particle that moves along the line segment from (1,0,0) to (3,4,2) in two ways: all alByusingmeparametuzaﬁmMesegmemto evaluate the work integral {\ b) By evaluating a potential function for F , x:1+2+ éC: \9,¢f£/ O\$+<( 5 5 i” Z 57/ W5: de: \$Ct®ﬂ+(x+g)49+(xW\Ag ”fé’ﬂql‘hdt + Zl+i+t%)w + (Haw 9924+ ,- a} jﬁwme): wwﬂeemh/qm/ 'b> ﬁsz? «Big—“XML” @kgz? z 7083’ r a”? W :37WC3 "\ :wtjlg1ﬁzm?x+g?+k/y 7, 195% HAW?) Ea Magi 70 % h/yzc Fine/mﬂ M » X—g}(4—M?+ C ’1" ST: MU NW’S'ﬂ/ﬂr) GED/Lazy 05.02%) For the vector field 2 sin(2x) F(x,y) = (4cos(2x)ln(y)+6x 3I+1 i+( y +9x2y2)j: ‘ f a) Prove that F is path independent A/ b) Find a potential function for F c) Evaluate the line integral L F. d 7where C is the line .1 i . segment from (6 ,1) to ( 4 ,2e) L __,' B” N gavel/x 5 Maﬁa ﬁg” ’ 752 z W ﬁwwl WWW 3 , . ﬂ [:4 eréX‘ﬂ-P/ 9 . w w b) max ‘5. @6333; 2241,9149 .+ 5 law +51% 93 1 2 MW ca 1/”) a» (37) QB. (14%) Use Green’s theorem to evaluate f0 (2xy + Data: + (y +x)dy, where C' Is the polygonal path (0, 0) to (3, 0) to (2,1) to (1,1) to (0,0). Sit/ﬂ 2131111 ...
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