Calculus 2 :

Section 7.3: Problem 12 (1 point) The region bounded by y = 6/(1 + '), y = 0, x = 0 and r = 2 is rotated about the line I = 2. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: and the function to be integrated is:Section 7.3: Problem 13 1 point) The region bounded by y = :" and y = sin(x/2) is rotated about the line I = -8. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: h and the function to be integrated is:Section 7.3: Problem 6 {1 point] um I Consider the blue horizontal line shown above [click on graph for better View} connecting the graphs :5 2 y} 2 sin(2y} and z 2 y} 2 cosy). Referring to this blue line, match the statements below about rotating this line with the corresponding statements about the result obtained. 1. The result of rotating the line about the zaxis is . The result of rotating The line about the yards is 3. The result of rotating the line about the line 3; = 1 is .The result ofrotating the line about the line 3 = 2 is 5. The result of rotating the line about the line 3 = it is . The result of rotating the line about the line 3,! = 2 is . The result of rotating the line about the line 3; = 1r 8. The result of rotating the line about the line 3; = 1r A. a cylinder of radius 3; and height msy) sint2y) B. an annulus with inner radius 2 i sin[2y) and outer radius 2 i oos(1y} C. a cylinder of radius 11r+ y and height oos[1y) sin[2y) I}. a cylinder of radius 1 y and height moy) sin[2y) E. a cylinder ofradius 2 + y and height cos[ly) sin(2y} F. a cylinder of radius 1r y and height cos[1y) sin(2y) G. an annulus with inner radius :r oosy} and outer radius :1- siny] is H. an annulus with inner radius siny) and outer radius oos{1y) Section 7.3: Problem 6 (1 point) x=Kys x=gly) X Consider the blue horizontal line shown above (click on graph for bet y (2y) and x = g(y) = cos(ly). Referring to this blue line, match the statements below about rotating but the result obtained. 1. The result of rotating the line about the r-axis is 2. The result of rotating the line about the y-axis is 3. The result of rotating the line about the line y = 1 is x=f(y) x=g(y) 4. The result of rotating the line about the line x = -2 is 5. The result of rotating the line about the line I = # is 6. The result of rotating the line about the line y = -2 is 7. The result of rotating the line about the line y = 8. The result of rotating the line about the line y = - A. a cylinder of radius y and height cos(ly) - sin(2y) B. an annulus with inner radius 2 + sin(2y) and outer radius 2 + cos(ly) C. a cylinder of radius + + y and height cos(ly) - sin(2y) D. a cylinder of radius 1 - y and height cos(ly) - sin(2y) E. a cylinder of radius 2 + y and height cos(ly) - sin(2y) F. a cylinder of radius * - y and height cos(ly) - sin(2y) G. an annulus with inner radius 7 - cos(ly) and outer radius x - sin(2y) is H. an annulus with inner radius sin(2y) and outer radius cos(ly)Section 7 6: Problem 1 (1 point) When a particle is located a distance I meters from the origin, a force of cos(x/7) newtons acts on it. Find the work done in moving the particle from = = 3 to I = 3.5. Find the work done in moving the particle from = = 3.5 to I = 4 Find the work done in moving the particle from = = 3 to x = 4Section 7 6: Problem 2 (1 point) A force of 5 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.8 feet beyond its natural length?]