# Determining the Volume of a Solid of Revolution - Page 3

Questions

- How do you use the method of cylindrical shells to find the volume generated by rotating the region bounded by #y=e^(−x^2)#, y=0, x=0, and x=1 about the y axis?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=6x^2#, #y=6sqrtx# rotated about the y-axis?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=x^2+1, y=-x^2+2x+5, x=0, x=3#, about the x axis?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y =x^3#, y= 8 , x= 0 revolved about the x-axis?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=6x+7# and #y=x^2# rotated about the line #y=49#?
- What is the volume of the solid produced by revolving #f(x)=xsinx, x in [0,pi] #around the x-axis?
- How do you find the volume of the solid #y=sqrt(9-x^2)# revolved about the x-axis?
- How do you find the volume of the region left of #y = sqrt(2x)# and below #y = 2# rotated about the y-axis?
- How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: y= x, #y = sqrt(x)#; about x = 2?
- How do you find the volume of the solid generated by revolving the region bounded by the curves #y = x-2#, the #x#-axis, #x=2#, and #x=4# rotated about the #x=-1#?
- How do you find the volume bounded by #y=sqrt(x + 1)#, x = 0, x = 3, and y = 0 revolved about the x-axis?
- How do you find the volume of the solid obtained by rotating the region bounded by the curves #y=x^2+1# and #y=-x+3# rotated around the x-axis?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y = 1 + x^2#, #y = 0#, #x = 0#, #x = 2# rotated about the y-axis?
- How do you find the volume of the solid generated by revolving the region bounded by the curves #y=2x^2#; y=0; x=2 rotated about the x-axis?
- What is the volume of the solid produced by revolving #f(x)=1/(x-1)-1/(x-2), x in [3,4] #around the x-axis?
- How do you find the volume of the region enclosed by the curves #y=2/x#, #y=0#, #x=1#, #x=3# rotated about #y=-1#?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=5e^(x)# and #y=5e^(-x)#, x = 1, about the y axis?
- How do you find the volume of the solid generated by revolving the region bounded by the curves y = 2x and y = x² rotated about the y-axis?
- Cylindrical shells (parts in details)?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y = 1/x^4#, y = 0, x = 1, x = 4 revolved about the x=-4?