# sample3 - x,y,z = t,t 2 0 ≤ t ≤ 1 6 A car is traveling...

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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 0 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 (
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Unformatted text preview: x,y,z ) = ( t,t 2 ), 0 ≤ t ≤ 1. 6. A car is traveling along a a curve y = x 2 from x = 0 to x = 1. At the position ( x,y ) the car’s speed is √ 1 + 4 x 2 . How much time does it take for the car to ﬁnish the journey? 7. Compute the integral H C xy 2 dx +( x 2 y + x ) dy where the curve C is the boundary of the rectangle with vertices (0, 0), (1, 0), (1, 1), and (0, 1) with counterclockwise orientation. 8. Compute the integral R C ydx + ( x + sin( e y )) dy along the curve y = sin x from x=0 to x=1. 1...
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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.

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