Final Exam Review

May 27th, 2016
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The University of Texas at Arlington
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Calculus 2 Exam review

Word Count: 2184
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Sketch the region bounded between the given curves and then find the area of the region.1) y = x2 , y = x32) x = y - y3 , x = 0Use shells to find the volume of the solid formed by revolving the given region about the y-axis.3) The region bounded by the curve y = x 3 , y-axis, and y = 14) The region bounded above by the graph of y = 2x - x 2 and below by the x-axisFind the volume of the solid formed by revolving the given region about the given line.5) The region bounded by the curves y = x2 and y = 4 about the line y = 4Solve the problem.6) Find the volume of the solid generated by revolving the region bounded by x = y2 and y = x2 about (a) thex-axis and (b) the y-axis.1Find the volume of the solid formed by revolving the given region about the given line.7) The region bounded by the graphs of y = x 2 and y = 2x about the line x = 2yxFind all points of intersection of the curves given.8) r = 2r = 2cos q.Solve the problem.9) Find the area enclosed by the graph of the polar equation r = sin q + cos q.10) Find the area enclosed by the graph of the polar equation r = 6 cos q.Find the length of the arc of the curve y = f(x) on the interval given.x3111) f(x) =+, on [1, 2]4x3Find the surface area generated when the graph of the function given on the prescribed interval is revolved about thex-axis.12) f(x) = 1 - x on [-1, 2]13) f(x) = x3 on [0, 1]

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