Volumes of solids of revolution - Disc method

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Intros
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Examples
Lessons
  1. The region bounded by the graphs of y=exy=e^x, y=0y=0,x=0x=0, and x=1x=1 is revolved about the x-axis. Find the volume of the resulting solid.
    1. Find the volume of the solid obtained by rotating the region bounded by x=3(y1)x=3\sqrt{(y-1)} , x=0x=0, and y=2y=2 about the y-axis.
      1. Find the volume of the solid obtained by rotating the region bounded by y=(x+1)y=\sqrt{(x+1)}, and y=1+x2y=\frac{1+x}{2} about the x-axis.
        1. Find the volume of the solid obtained by rotating the positive region bounded by y=x3y=x^3, y=xy=x
          1. about y=3y=3
          2. about x=2 x=-2
        2. Find the volume of the solid obtained by rotating the region bounded by y=3cosxy=3-cosx, and y=4y=4 about y=1y=1.