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# 2423_test1 - y 2-y = x and y = x 4 IV(20 pts Find the...

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NAME: 1 Math 2423, Test I September 29, 2004 Show all your work to receive full credit. The use of books and notes is not allowed. Good luck! I. (20 pts) Estimate the area under the graph of f ( x ) = 1 + 1 x from x = 1 to x = 5 using 4 approximating rectangles and right endpoints.

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2 II. (20 pts) Find the indefinite integrals a) R ( y + 1 y ) 2 dy ; b) R cos x cos(sin x ) dx ; c) R x x 2 +1 dx ; d) R y y - 1 dy .
3 III. (20 pts) Find the area of the region bounded by the curves

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Unformatted text preview: y 2-y = x and y = x . 4 IV. (20 pts) Find the volume of the solid obtained by rotating the region bounded by y =-x 2 + 2 x and y = 0 about the line x = 3. 5 V. (20 pts) An aquarium 2 m long, 1 m wide and 2 m deep is half full of water. Find the work needed to pump all the water out of the aquarium. (Use ρ water = 1000 kg/m 3 and g = 10 m/sec 2 )....
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