Exam 4 Spring11 - Z 3 Z √ 9-y f ( x,y ) dxdy . 9. SET UP...

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MAC 2313-EXAM 4 NAME UF ID 1. A lamina occupies the part of the disk x 2 + y 2 1 in the first quadrant. Find the mass if the density at any point is proportional to its distance to the y axis. 2. SET UP (Do not evaluate) the integral Z 2 - 2 Z 4 - y 2 - 4 - y 2 Z 2 x 2 + y 2 ( x 2 + y 2 ) z dz dxdy in cylindrical coordinates. 3. Let H be the region between the sphere x 2 + y 2 + z 2 = 4 and x 2 + y 2 + z 2 = 9 in the first octant then the region H in sphererical coordinates is given by . H = { ( ρ,θ.φ ) : } 4. Let E be the region bounded by the paraboloid z = 4 x 2 + 4 y 2 and the plane z = 4, then the region E in Cartesian coordinates is given by E = { ( x,y,z ) : } 5. According to Fubini’s theorem, if f is continuous on the rectangle R = { ( x,y ) | a x b,c y d } then ZZ R f ( x,y ) dA = = 1
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6. Calculate the iterated integral Z 2 0 Z π 0 r sin 2 θdθdr . 7. Given the integral ZZ D ( x + y ) dA = Z 1 0 Z 2 - y 2 y ( x + y ) dxdy , the region D in polar coordinates is given by D = { ( r,θ ) : } 8. Change the order of integration for
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Unformatted text preview: Z 3 Z √ 9-y f ( x,y ) dxdy . 9. SET UP (Do not evaluate) the integral Z Z D ( x + y ) dA , where D is bounded by y = √ x and y = x 2 . 10. If R = 0 ≤ x ≤ 6 , ≤ y ≤ 4 } and m = 3 ,n = 2 and we would like to use the upper right corners of the squares, write all sample points that would be used to calculate the double Riemmann sum. 2 MAC 2313 — EXAM 4 Free Response NAME UF ID YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE CREDIT!! 1. Evaluate the integral Z 1 Z √ 2-y 2 y ( x + y ) dxdy 3 2. Find the volume of the solid that lies within the sphere x 2 + y 2 + z 2 = 4, above the xy plane, and below the cone z = p x 2 + y 2 . 4...
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This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.

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Exam 4 Spring11 - Z 3 Z √ 9-y f ( x,y ) dxdy . 9. SET UP...

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