Practice Test IV C for Math 1501, Calculus IProblem 1:Let Ω be the region in thex, yplane bounded by:y=x4y= 4x2(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 linex= 0.(d) Find the volume of the body produced by rotating this region about the linex= 3.Problem 2:a) A flagpole that is 10 m long, that has a uniform mass density of 1kg/mis 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 densityρ(x) = 2-x10kg/m,wherexis the distance from the base. How much work is done in raising the flagpole thistime?Problem 3:A doughnut whose precise dimension is given below, is covered by a layer of
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