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Compute the volume of the solid of revolution generated by f(x) = x^(1/2)

Sketch the graph and compute the volume of the solid of revolution generated by:

    \[ f(x) = \sqrt{x}, \qquad \text{on} \qquad 0 \leq x \leq 1. \]


The sketch of the ordinate set of f(x) = \sqrt{x} on [0,1] is as follows:

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We then compute the volume of the solid of revolution.

    \[  V = \int_0^1 \pi x \, dx = \pi \left. \frac{x^2}{2} \right|_0^1 = \frac{\pi}{2}. \]

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