Volume: disk/washer method:   Lecture Video 1   Lecture Video 2

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  1. Find the volume of the solid obtained by rotating the region bounded by \(y=\sqrt{x}, \: x=4 \) and \(x\)-axis about the \(x\)-axis.  solution

  2. Find the volume of the solid obtained by rotating the region bounded by \(y=\sqrt{x}\) and \(y=x\) about the \(x\)-axis. solution

  3. Sketch the region enclosed by the graphs of \(y=x^2\) and \(y=3x\). Now use a definite integral to find the volume of revolution obtained by rotating the region about \(x\)-axis.  solution

  4. Find the volume of the solid of rotation of the region enclosed by the curves \(y=x, \: y=x+2, \: x=0, \: x=2\) about the \(x\)-axis. solution

  5. Find the volume of the solid of rotation of the region enclosed by the curves \(y=2+e^x, \: y=1, \: x=0, \: x=2\) about the line \(y=0\). solution