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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
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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
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b) Set up integrals to ﬁnd the center of mass of the lamina, but do NOT evaluate.
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. (12 points) Evaluate LL]; 1le + y2 dxdy by converting to polar coordinates ’5 .. -A F-r-v—rﬁgg—E? H. re—ﬁ mmw‘ x
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: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.
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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
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