Donnie Smith Assignment Section 7.3 due 04/17/2017 at 11:59pm MST 4. (1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 1. (1 point) Find the volume of the solid obtained by rotating the region bounded by 2 y = 4 sin(9x ), r y = 0, 0x Sharma MAT 266 ONLINE B Spring 2017 y = 1/x4 , , 9 y = 0, x = 2, x = 5; about the y-axis. Volume = about the y axis. Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 2. (1 point) Use the method of cylindrical shells to find the volume gen2 erated by rotating the region bounded by y = ex , y = 0, x = 0, and x = 1 about the y-axis. Volume = Answer(s) submitted: (incorrect) 3. (1 point) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 2 + x x2 and y + x = 2 about the y-axis. Below is a graph of the bounded region. 5. (1 point) Consider the blue vertical line shown above (click on graph for better view) connecting the graphs y = g(x) = sin(2x) and y = f (x) = cos(3x). Referring to this blue line, match the statements below about rotating this line with the corresponding statements about the result obtained. 1. 2. 3. 4. 5. 6. 7. 8. Volume = Note: You can click on the graph to enlarge the image. The result of rotating the line about the x-axis is The result of rotating the line about the y-axis is The result of rotating the line about the line y = 1 is The result of rotating the line about the line x = 2 is The result of rotating the line about the line x = is The result of rotating the line about the line y = 2 is The result of rotating the line about the line y = The result of rotating the line about the line y = A. a cylinder of radius x + 2 and height cos(3x) sin(2x) B. an annulus with inner radius sin(2x) and outer radius cos(3x) C. an annulus with inner radius + sin(2x) and outer radius + cos(3x) Answer(s) submitted: (incorrect) 1 D. an annulus with inner radius cos(3x) and outer radius sin(2x) E. a cylinder of radius x and height cos(3x) sin(2x) F. a cylinder of radius x and height cos(3x) sin(2x) G. an annulus with inner radius 1 cos(3x) and outer radius 1 sin(2x) is H. an annulus with inner radius 2 + sin(2x) and outer radius 2 + cos(3x) a cylinder of radius + y and height cos(4y) sin(1y) a cylinder of radius y and height cos(4y) sin(1y) a cylinder of radius 1 y and height cos(4y) sin(1y) an annulus with inner radius 2 + sin(1y) and outer radius 2 + cos(4y) F. a cylinder of radius 2 + y and height cos(4y) sin(1y) G. a cylinder of radius y and height cos(4y) sin(1y) H. an annulus with inner radius cos(4y) and outer radius sin(1y) is B. C. D. E. Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 6. (1 point) 7. (1 point) Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves x2 y2 = 7 and x = 4 about the line y = 5 ? Z 3 p A. 2(y 5)(4 y2 + 7) dy Z 3 3 p B. 2(y + 5) y2 + 7 dy Z3 4 p C. 2(5 y)(4 y2 + 7) dy Z 37 p D. 2(5 y)(4 y2 + 7) dy Z 3 4 p E. 2(y + 5) y2 + 7 dy Z 47 p F. 2(y 5)(4 y2 + 7) dy 7 Answer(s) submitted: Consider the blue horizontal line shown above (click on graph for better view) connecting the graphs x = f (y) = sin(1y) and x = g(y) = cos(4y). Referring to this blue line, match the statements below about rotating this line with the corresponding statements about the result obtained. 1. 2. 3. 4. 5. 6. 7. 8. A. (incorrect) 8. (1 point) Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y = x and y = 4x x2 about the line x = 6 ? Z 3 \u0002 \u0003 2(6 x) x (4x x2 ) dx A. The result of rotating the line about the x-axis is The result of rotating the line about the y-axis is The result of rotating the line about the line y = 1 is The result of rotating the line about the line x = 2 is The result of rotating the line about the line x = is The result of rotating the line about the line y = 2 is The result of rotating the line about the line y = The result of rotating the line about the line y = an annulus with inner radius sin(1y) and outer radius cos(4y) B. C. D. E. Z03 Z0 3 Z0 4 Z 04 0 2 \u0002 \u0003 2(6 x) (4x x2 ) x dx \u0002 \u0003 2(x 6) (4x x2 ) x dx \u0002 \u0003 2(6 x) x (4x x2 ) dx \u0002 \u0003 2(x 6) (4x x2 ) x dx F. Z 4 \u0002 \u0003 2(6 x) (4x x2 ) x dx D. 0 Answer(s) submitted: E. (incorrect) F. (incorrect) 12. (1 point) The region bounded by y = 2/(1 + x2 ), y = 0, x = 0 and x = 8 is rotated about the line x = 8. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: a= b= and the function to be integrated is: Answer(s) submitted: (incorrect) 13. (1 point) The region bounded by y = x8 and y = sin(x/2) is rotated about the line x = 4. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: 10. (1 point) Which of the following integrals represents the volume of the solid p obtained by rotating the region bounded by the curves x = sin(y), 0 y 2, and x = 0 about the line y = 9 ? Z 1 p A. 2(y + 9) sin(y) dy Z0 p B. 2(y + 9) sin(y) dy Z0 p C. 2(9 y) sin(y) dy Z0 1 p D. 2(y 9) sin(y) dy Z 0 p E. 2(y 9) sin(y) dy Z 01 p F. 2(9 y) sin(y) dy a= b= and the function to be integrated is: Answer(s) submitted: (incorrect) 14. (1 point) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y = x2 , y = 0, x = 1, and x = 2 about the line x = 4. Volume = 0 Answer(s) submitted: (incorrect) Answer(s) submitted: 11. (1 point) Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y = ln(x), y = 0, and x = 2 about the y-axis? C. Z 2 Z12 (incorrect) 15. (1 point) The region between the graphs of y = x2 and y = 3x is rotated around the line x = 3. The volume of the resulting solid is 2(x 2) ln(x) dx Answer(s) submitted: 2(x 2) ln(x) dx 2 (incorrect) 2 ln(x) dx 0 2x ln(x) dx (incorrect) Z0 2x ln(x) dx Z 12 Answer(s) submitted: Answer(s) submitted: B. 2 ln(x) dx Z 12 0 9. (1 point) Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y = 1/(1 + x2 ), y = 0, x = 0, and x = 4 about the line x = 4 ? \u0013 \u0012 Z 4 1 dx A. 2(4 + x) 2 0 \u00121+x \u0013 Z 4 4 B. 2(x 4) dx 2 0 \u00121+x \u0013 Z 4 4 dx C. 2(4 + x) 2 0 \u00121 + x \u0013 Z 4 4 D. 2(4 x) dx 1 + x2 \u0013 0 \u0012 Z 4 1 dx E. 2(x 4) 1 + x2 \u0013 0 \u0012 Z 4 1 F. 2(4 x) dx 1 + x2 0 A. Z 2 3 c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 4