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# Test 4b - meters to a height of 6 meters Assume that the...

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Test IV for Calculus I, Math 1501E1, November 19, 2002 Name: This test is to be taken without calculators and notes of any sorts. The allowed time is 50 minutes. Provide exact answers; not decimal approxi- mations! For example, if you mean 2 do not write 1 . 414 . . . . Show your work, otherwise credit cannot be given.

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I: (25 points) Calculate the indefinite integrals a ) Z ( x + 3) 4 x d x b ) Z x ( x + 2) 1 / 3 d x c ) Z x 3 (1 - x 4 ) - 1 / 4 d x Compute the definite integrals d ) Z 1 0 x + 4 x + 2 d x e ) Z π/ 2 - π/ 2 p 1 + cos( x ) sin( x )d x
II: (25 points) Consider the region that is bounded by the two parabolas y = 3 x 2 and x = 3 y 2 . a) Calculate the area of this region. b) Calculate the centroid of this region.

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III: (25 points) Consider a ramp, made out of rock, whose base is 100 meters long, 20 meters wide and ascends linearly from the ground (i.e., 0
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Unformatted text preview: meters) to a height of 6 meters. Assume that the density of the building material is 5000kg / m 3 and that the gravitational acceleration is 10m / s 2 . a) Calculate the work needed to construct the ramp. b) How long will it take at least to construct this ramp if one uses a 10 horse power machine to lift the material ? (1 horse power =750 Watts). IV: (25 points) Consider the region R that is bounded above y = √ 2-x , below by the x axis and on the side by x = 0 and x = 1. a) Calculate the volume of the solid that is generated by rotating R about the y axis. b) Calculate the volume of the solid generated by revolving the region R about the x axis....
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Test 4b - meters to a height of 6 meters Assume that the...

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