Applications of Integration Test Form A. Determine the area of the region bounded by the graphs of y x 4x and y x 4. (a) 9 9 (b) 6 (c). Find the volume of the solid formed by revolving the region bounded by the graphs of y x, y and x about the x-axis. 7 4 (a) 7 (b) 7 (c) 7. Which of the following integrals represents the volume of the solid formed by revolving the region bounded by the graphs of y x, y and x about the line x? (a) yy (b) dy x dx (c) xx dx 4. Find the volume of the solid formed by revolving the region bounded by the graphs of y x 4x and y about the y-axis. y dy 544 (a) (b) (c) 5 4 6 6 5. Identify the definite integral that represents the arc length of the curve y x over the interval,. (a) (b) (c) x dx x dx 4x dx x dx
Test Bank 6. Identify the definite integral that represents the area of the surface formed by revolving the graph of fx x on the interval, about the x axis. (a) x x 4 dx (b) x 4x dx (c) y y dy x 4x dx 7. A force of pounds stretches a spring 4 foot on an exercise machine. Find the work done in stretching the spring foot. (a) ft-lb (b) 5 ft-lb (c) ft-lb 4 ft-lb 9. Find the x-coordinate of the centroid of the region bounded by the graphs of y x, y and x. (a) 7 (b) 4 (c) 4 7
Applications of Integration Test Form B. Determine the area of the region bounded by the graphs of y x x and y. (a) 4 9 (b) (c) 4. Find the volume of the solid formed by revolving the region bounded by the graphs of y x, x and y about the y-axis. 9 47 (a) 5 (b) 7 (c) 5 6 5. Which of the following integrals represents the volume of the solid formed by revolving the region bounded by the graphs of y x, y and x about the line y? (a) y y dy (b) x dx (c) x dx y y dy 4. Find the volume of the solid formed by revolving the region bounded by the graphs of and y about the y-axis. y x 64 (a) (b) (c) 5 5. Identify the definite integral that represents the arc length of the curve y x over the interval,. (a) ln x dx (b) x dx (c) x 4 dx x x 4 dx
Test Bank 6. Identify the definite integral that represents the area of the surface formed by revolving the graph of fx x on the interval, about the y-axis. (a) x 9x 4 dx (b) x 9x 4 dx (c) x x dx x x dx 7. A force of pounds compresses a spring inches. How much work is done on compressing the spring 6 inches? (a) 4 in-lb (b) 6 in-lb (c) 4 in-lb in-lb. Find the y-coordinate of the centroid of the region bounded by the graphs of y x, y and x. 4 (a) 5 (b) 5 (c) 4 5
4 Applications of Integration Test Form C A graphing calculator is needed for some problems. b. The integral sin x e x dx computes the area of a region between two curves. a Use a graphing calculator to estimate the value of a. (a) (b). (c)..6. Use a graphing calculator to graph the region bounded by the graphs of y x x, y, and x. Then use calculus to compute the volume of the solid formed by revolving this region about the x-axis. 4 7 (a) (b) (c) 97 6. Use the integration capabilities of a graphing calculator to approximate the volume of the solid formed by revolving the region bounded by the graphs of y sin x and y in the interval, about the y-axis. Round your answer to three decimal places. (a).6 (b) 4.95 (c) 9.79.4 4. Use the integration capabilities of a graphing calculator to approximate the arc length of the graph of fx cos xon the interval,. Round your answer to three decimal places. (a) (b). (c).4.4 5. Use the integration capabilities of a graphing calculator to approximate the area of the surface formed by revolving the graph of fx sin x on the interval, about the y-axis. Round your answer to three decimal places. (a) 6. (b) 7.74 (c). 4.44 6. A force of 5 pounds compresses a spring 5 inches from its natural length. Find the work done in compressing the spring additional inches. [Units are in inch-pounds.] (a),5 (b) 5 (c),
Test Bank 5 7. Use the Theorem of Pappus to find the volume of the solid of revolution of the torus formed by revolving the circle x y 4 about the x-axis. (a) (b) (c) 6 4 4. Find the centroid of the region bounded by the graphs of fx x and gx 4 (a) 4 (b), (c) 6, 6, 45, x. 4
6 Applications of Integration Test Form D. Find the area of the region bounded by the graphs of y x and x y 5.. Find the volume of the solid formed by revolving the region bounded by the graphs of y e x, y, x, and x about the x-axis.. Use the shell method to set up the integral that represents the volume of the solid formed by revolving the region bounded by the graphs of y x and x y 5 about the line y. (Do not evaluate the integral.) 4. Find the volume of the solid formed by revolving the region bounded by the graphs of y x and y 4 about the x-axis. 5. Write the definite integral that represents the arc length of one period of the curve (Do not evaluate the integral.) y sin x. 6. Write the definite integral that represents the area of the surface formed by revolving the graph of fx x on the interval, 4 about the y-axis. (Do not evaluate the integral.) 7. A force of 4 pounds compresses a -inch spring by inches. How much work is done in compressing the spring to a final length of 4 inches?. Find the centroid of the region bounded by the graphs of y x, y, and x.
Test Bank 7 Test Form E A graphing calculator is needed for some problems. b a. The integral ln x x dx computes the area of a region between two curves. a. Use a graphing calculator to graph the curves y ln x and y x. b. Use the graph to estimate the values of a and b. c. Use the integration capabilities of a graphing calculator to approximate the area of the region. Round your answer to three decimal places.. Use the integration capabilities of a graphing calculator to approximate the volume of the solid formed by revolving the region bounded by the graphs of y ln x, x y, and the x-axis about the x-axis. Round your answer to three decimal places.. Consider the region bounded by the graphs of y y x, and x. x, a. Sketch the region described. b. Find the point(s) of intersection. c. Calculate the volume of the solid formed when this region is revolved about the line x. 4. A telephone wire suspended between two poles forms a catenary modeled by the equation x y cosh, 5 x 5 where x and y are measured in feet. Approximate the length of the suspended cable if the poles are feet apart. 5. Neglecting air resistance, determine the work done in propelling a -ton satellite to a height of miles above the surface of the earth. 6. A circular observation window on a cruise ship has a radius of foot and the center of the window is feet below water level. What is the fluid force on the window? (Use 64 lbft as the weight-density of sea water.) 7. Consider the plane region bounded by the graphs of fx x and gx. a. Calculate the moment about the x-axis. b. Find the centroid of the region. c. Find the volume of the solid formed by revolving the region about the x-axis using the Theorem of Pappus. d. Use disc method to find the volume described in part c.. Use the integration capabilities of a graphing calculator to approximate the centroid of the region bounded by the graphs y ln x and y. Round your answer to three decimal places.