Multiple Choice (5 points each)



Multiple Choice. You may use a Calculator.1. Identify the definite integral(s) that represents the area of the region bounded by the graphs of and .a. b. c. d. e. None of these2. Which of the following integrals represents the volume of the solid formed by revolving the region bounded by the graphs of , , and about the line ?a. b. c. d. e. None of these3. The base of a solid is the region in the first quadrant bounded by the line and the coordinate axes. What is the volume of the solid if every cross section perpendicular to the y-axis is a square. a. 15.75b. 36c. 18d. 72e. None of these4. Find the area of the region bounded by the graphs of the equations and over the interval .a. b. c. d. e. 4602480-1765305. Consider and .a. Sketch a graph of the region(s) bounded by the two curves. b. Determine the points of intersection. c. Set up the integrals needed to find the area of the regions bounded by the two curves. Use the graphing capabilities to find the area bounded by these curves. Free Response: A Graphing Calculator may be used.37071304959356. Consider the regions bounded by the curves and . a. Use a graphing utility to graph the curves and . b. Use a graphing utility to find the coordinates of the points of intersection. c. Write the integral and use the integration capabilities of a graphing utility to approximate the area of the region. Round your answer to three decimal places. d. If this region were the base of a solid in which cross sections taken perpendicular to the x-axis were always an equilateral triangle, set up the integral that would be used to find its volume. Do not evaluate. (Hint: The area of an equilateral triangle with sides s is )Multiple Choice: No Calculator May Be Used. 7. Identify the definite integral that computes the volume of the solid generated by revolving the region bounded by the graph of , and the line , between and about the line.a. b. c. d. e. None of theseFree Response. No Calculator May Be Used. 51816001365258. Consider and graphed below. a. Find the points of intersection of the graphs of f and g. (2 points) b. Set up the integral that would be used to calculate the area of the region. (3 points)c. Use the shell method to set up the integral that would be used to calculate the volume of the solid produced by revolving the region about the line y = -4. d. Use the disc method to set up the integral that would be used to calculate the volume of the solid produced by revolving the region about the x = -7. 9. Consider the region bounded by , , from to .369760515875a. Graph the curve. b. Set up an integral that can be used to find the volume of the solid created by revolving the region about the line . c. Set up an integral that can be used to find the volume of the solid created by revolving the region about the line .d. If this region were the base of a solid in which cross sections taken perpendicular to the x-axis were always semi-circles, set up the integral that would be used to find its volume. ................
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