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The University of Memphis MATH 1920 Summer 2011 Calculus II Dwiggins

The University of Memphis MATH 1920 Summer 2011 Calculus II Dwiggins. FINAL EXAM There are 12 questions worth ten points each. Part I – Techniques of Integration. # 1. Find the following antiderivatives:. (a). (b). # 2. Calculate the following definite integrals:. (a).

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The University of Memphis MATH 1920 Summer 2011 Calculus II Dwiggins

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  1. The University of Memphis MATH 1920 Summer 2011 Calculus II Dwiggins FINAL EXAM There are 12 questions worth ten points each. Part I – Techniques of Integration # 1. Find the following antiderivatives: (a) (b) # 2. Calculate the following definite integrals: (a) . (b)

  2. Page 2 Calculus II Final Exam # 3. Find the following antiderivatives: (a) . (b) Part II – Geometric Calculations # 4. (a) Sketch the region D bounded by the x-axis, the curve (b) Show that two integrals are required to calculate the area of D using vertical strips, while only one integral is required if horizontal strips are used to partition D. (c) Calculate the area of D using whichever method is easiest.

  3. Page 3 Calculus II Final Exam # 5. Let D represent the region bounded by the y-axis, the line y = 4, and the curve x = y2. Calculate the volume obtained when D is revolved about: (a) the x-axis (b) the y-axis # 6. Calculate the centroid of D, and use a theorem of Pappus to calculate the volume obtained when D is revolved about the line x = 4.

  4. Page 4 Calculus II Final Exam (b) Let C denote the curve y = x2 , 0 <x< 1. Calculate the surface area obtained by revolving C about the y-axis. Part III – Series and Approximation # 8. Determine the interval of convergence for the power series

  5. Page 5 Calculus II Final Exam # 9. Give the power series (with x0 = 0) for each of the following functions, and give the interval of convergence for each series. (a) (b) (c) Part IV – Analytic Geometry # 10. Classify each of the following as the equation for an ellipse, a parabola, or a hyperbola. (a) (b) (c) (d) (e)

  6. Page 6 Calculus II Final Exam # 11. Sketch the graph of the polar curve and calculate the area bounded by this curve. # 12. Consider the curve given parametrically by Fill in the following chart of values, indicating where the tangent line is either vertical or horizontal, and use this information to sketch the trajectory. y x What are the slopes of the tangent lines at the point where the curve crosses itself? Show that the second derivative tells us this curve is concave up for –1 < t < 1 and concave down otherwise.

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