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Unformatted text preview: Name: Score: Math 137 Sample Test III 1. (10pts) Find the volume under the surface x + y + z = 10 and over the region D bounded by y = 0 and y = x 3 , 0 ≤ x ≤ 1. 2. (20pts) Compute the integral Z 1 1 dx Z 1 x 2 dyx 9 ln( y 5 + 1) . 3.(20pts) Compute the integral Z Z Z ( x + y ) dxdydz where V is the body bounded from above by the upper semisphere x 2 + y 2 + z 2 = 1 and from below by z = x 2 + y 2 . 4. (20 pts) An oil reservior has a shape of a sphere x 2 + y 2 + z 2 ≤ 1 . Drilling samples show that the density function for the oil in the reservior is f ( x,y,z ) = z + 10 pounds per cubic feet. Find the total weight of oil in the reservior. 5(20pts). Calculate Z C ( x + y ) dx + ( x 2 y 2 ) dy where the curve C is ( x,y,z ) = ( t,t 2 ), 0 ≤ t ≤ 1. 6. and later. see my last email. 1 Rough answers 1. The volume is Z Z D ((10 x y ) dxdy = Z 1 dx Z x 3 dy (10 x y ) = ..... = 5 / 2 1 / 5 1 / 14 = .......
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This note was uploaded on 03/10/2010 for the course MATH 137 taught by Professor Phann during the Fall '09 term at Georgetown KY.
 Fall '09
 Phann
 Math, Multivariable Calculus

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