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Practice Test 4c - Practice Test IV C for Math 1501...

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Practice Test IV C for Math 1501, Calculus I Problem 1: Let Ω be the region in the x, y plane bounded by: y = x 4 y = 4 x 2 (a) Find the area of this region. (b) Find the centroid of this region. (c) Find the volume of the body produced by rotating this region about the line x = 0. (d) Find the volume of the body produced by rotating this region about the line x = 3. Problem 2: a) A flagpole that is 10 m long, that has a uniform mass density of 1 kg/m is initially lying down and is stood up on its end. How much work is done? b) Now suppose that the flagpole is tapered with a mass density ρ ( x ) = 2 - x 10 kg / m , where x is the distance from the base. How much work is done in raising the flagpole this time? Problem 3: A doughnut whose precise dimension is given below, is covered by a layer of
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