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# Test 4a - lengthwise and is constant across The pool is...

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Test IV for Calculus I, Math 1501C1, 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 + 1) 3 x d x b ) Z x 1 + x d x c ) Z exp( x 3 ) x 2 d x Compute the definite integrals d ) Z 1 0 x + 2 x + 1 d x e ) Z π/ 2 - π/ 2 p cos( x ) sin( x )d x
II: (25 points) Consider the region that is bounded by the curves y = x 2 and y = x 3 - x 2 . a) Calculate the area of this region. b) Calculate the centroid of this region.

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III: (25 points) A swimming pool is 50 meters long and 20 meters wide. Its bottom decreases linearly from a depth of 0 meter to a depth of 3 meters
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Unformatted text preview: lengthwise and is constant across. The pool is completely Flled with water. The density of water is 1000kg / m 3 and the gravitational acceleration is 10m / s 2 . a) Calculate the work needed to empty the pool. b) How long will it take for a 10 horse power pump to empty the pool? (1 horse power =750 Watts). IV: (25 points) Consider the region R that is bounded above y = √ 1 + 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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