# Applications of the Integral

### Problems

Problem : Apply the disk method to find the volume of the unit sphere obtained by revolving the region below the graph of f (x) = from x = - 1 to 1 about the x -axis.

Problem : Apply the shell method to find the volume of the solid obtained by revolving the region below the graph of f (x) = x 2 from x = 0 to 1 about the y -axis (this solid looks like a cylinder with a bowl carved out of the top).

Problem : Compute the volume of the square pyramid with base in the x = 0 plane with sides of length 10 and vertex at the point (5, 0) , using the cross-sectional area method.

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