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C3T3V2SolutionsSpring08

# C3T3V2SolutionsSpring08 - Sol uh‘onS MA 242 Test 3...

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Unformatted text preview: Sol uh‘onS MA 242- Test 3 Version 2 NO WORK=NO CREDIT! l. (12 points) Evaluate the iterated integral ﬁwéxy dz dy dx 3. (15 points) A lamina occupies a region D = {(x,y)| O S x S 3, O S y S I and has a density function p(x,y) = 4y a) Find the mass of the lamina ' , l; mzﬁggﬁ 974.7dxtf63272/0K4X :LBZXCJX :X2/jrm b) Set up integrals to ﬁnd the center of mass of the lamina, but do NOT evaluate. S, w '3 w _ 2 u? x)47>:(.m_:\i)l‘%\ :(quﬁxﬂdﬂdgygw 4. (12 points) Evaluate EL: ‘ ‘y ‘7 1/x2 + y2 dxdy by converting to polar coordinates ioffz '- TILTBIZA€J {gs rzokrde'g; 5 O O :X’T 3 5. (15 points) Suppose that E is the solid tetrahedron formed by the planes X = 0, y = O, z = 0, 6. (15 points) Use spherical coordinates. Suppose E is the solid that lies between the spheres x2 + y2 + 22 = 4 and x2 + y2 + z2 = 6 in the ﬁrst octant. Set up HIEf(x,y,z)dV, do NOT evaluate. a»; m we r; I meﬂdlf y _ _-...—..———.—-——ﬁ——.. —. ;.—-qr.n—_-nw-ww——-w—nv—. . <. -— -m; Tum‘r-S r—VL‘F 3."? 7. (15 points) Use cylindrical coordinates to set up a triple integral [do NOT evaluate] to ﬁnd the volume of the region E, where E lies under 2 =11- x2 - y2 and above 2 = 2, and inside x2 + y2 =1. l: y ._ I ._ .._..._:g -. _._ A «3....-- .u—u_______ Extra Credit (3 points): Use cylindrical coordinates to set up a triple integral [do NOT evaluate] to find the volume of the region E, where E lies under 2 =11- x2 — y2 and above 2 =2, and outside x2 + y2 =1. . r __ Z __ r 7 a u—tAyz— u-r ~ 2 s q z: (’2 r : 5 X 8. (4 points) Finish the Integration by Parts formula I udV = [AV " ...
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C3T3V2SolutionsSpring08 - Sol uh‘onS MA 242 Test 3...

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