# Calculating Volume using Integrals - Page 3

Questions

- How do you find the area enclosed by #y=sin x# and the x-axis for #0≤x≤pi# and the volume of the solid of revolution, when this area is rotated about the x axis?
- How do you find the volume of a solid that is enclosed by #y=secx#, #x=pi/4#, and the axis revolved about the x axis?
- How do you find the volume of the solid with base region bounded by the triangle with vertices #(0,0)#, #(1,0)#, and #(0,1)# if cross sections perpendicular to the #x#-axis are squares?
- How do you find the volume of a solid that is enclosed by #y=-x^2+1# and #y=0# revolved about the x-axis?
- The region under the curves #y=cosx-sinx, 0<=x<=pi/4# is rotated about the x axis. How do you sketch the region and find the volumes of the two solids of revolution?
- The region under the curve #y=sqrt(x^2-4)# bounded by #2<=x<=4# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?
- How do you find the volume V of the described solid S where the base of S is a circular disk with radius 4r and Parallel cross-sections perpendicular to the base are squares?
- Derive the formula for the volume of a sphere?
- How do you find the volume of a rotated region bounded by #y=sqrt(x)#, #y=3#, the y-axis about the y-axis?
- The region under the curves #y=e^(1-2x), 0<=x<=2# is rotated about the x axis. How do you sketch the region and find the volumes of the two solids of revolution?
- How do you find the volume of a pyramid using integrals?
- How do you find the volume of the region bounded by the graph of #y = x^2+1# for x is [1,2] rotated around the x axis?
- How do you find the volume of the solid bounded by the coordinate planes and the plane 6x + 5y + z = 6?
- How do you find the volume of the solid formed when the area in the first quadrant bounded by the curves #y=e^x# and x = 3?
- The region under the curves #y=sinx/x, pi/2<=x<=pi# is rotated about the x axis. How do you find the volumes of the two solids of revolution?
- How do you find the volume of the parallelepiped determined by the vectors: <1,3,7>, <2,1,5> and <3,1,1>?
- Let R be the region in the first quadrant enclosed by the graphs of #y=e^(-x^2)#, #y=1-cosx#, and the y axis, how do you find the volume of the solid generated when the region R is revolved about the x axis?
- How do you find the volume of the solid that lies within the sphere #x^2+y^2+z^2 =25#, above the xy plane, and outside the cone?
- The region under the curve #y=sqrtx# bounded by #0<=x<=4# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?
- Let R be the region in the first quadrant enclosed by the lines #x=ln 3# and #y=1# and the graph of #y=e^(x/2)#, how do you find the volume of the solid generated when R is revolved about the line y=-1?