C3T3V1SolutionsSpring08

C3T3V1SolutionsSpring08 - So 5 1003 MA 242 Test 3 Version 1...

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Unformatted text preview: So! 5 [+1003 MA 242- Test 3 Version 1 NO WORK=NO CREDIT! 1 z x 1. (12 points) Evaluate the iterated integral Jo Jo In +z6xz dy dx dz Kiri—l 1; So EéXZ‘jlo $de :f yo? éXZ(><+E)Q><dE 1.3....” mm fig#N—-c’=< _-.-. flu—1v A f 1 H 5:30 o“) 63 m .. ‘XFJ ‘ N f} Q2 W p O. x O.— 9‘ i l 3 2 2. (12 points) Evaluate LL ey dydx by reversing the order of integration. ,f” 3. (15 points) A lamina occupies a region D = {(x,y)| 0 S x S 2, 0 S y S .J; } and has a density function p(x,y) =12y3 __ a) Find the mass of the lamina r - 2 \J“ S 2 K M—f f X ; vf a! CL 0 0 ’2vd74X 657 a K : 2 _ 3/2: f0 3K2<21>< ~ >< 6 E b) Set up integrals to find the center of mass of the lamina, but do NOT evaluate. ,_ - Lo 2141 £20 W1213de'clx fazfgwlztfiaj ac :Er-qT—T ~74:q?—m—W—W*w.qewww— w-H—fi— , 3 9- 2 . (12 points) Evaluate LL]; 1le + y2 dxdy by converting to polar coordinates ’5 .. -A F-r-v—rfigg—E? H. re—fi mmw‘ x H H fly.) a =2 W ‘QWQW nil 9"? a/Q/ GD‘r Q, G) l) 3/) 2} .D 9% n A) :1 SW- ,_=—= .W , ‘ ”A. _ mu?“ , V .F _ g 5-:— “my? 5. (15 points) Suppose that E is the solid tetrahedron formed by the planes x = 0, y = 0, z = 0, and 3x +2y +z = 6. Set up, but do NOT evaluate HIE x32 dV. Show all of your work. E (010) 4» 6. (15 points) Use spherical coordinates. Suppose E is the solid that lies between the spheres x2 + y2 + z2 = 3 and x2 + y2 + z2 =16 in the first octant. Set up IflEf(x,y,z)dV, do NOT evaluate. r 7. (15 points) Use cylindrical coordinates to set up a triple integral [do NOT evaluate] to find the volume of the region B, where E lies under z = 12- x2 - y2 and above 2 = 8, and inside it2 + y2 =1. Extra Credit (3 points): Use cylindrical coordinates to set up a triple integral [do NOT evaluate] to find the volume of the region B, where E lies under 2 =12 - x2 — y2 and above 2 = 8, and outside it2 + y" =1. 8. (4 points) Finish the Integration by Parts formula JudV = UV '- SV AM i l rvm 93*. .4 ...
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