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Compute the volume of the solid of revolution generated by f(x) = cos x

by RoRi

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

    \[ f(x) = \cos x, \qquad \text{on} \qquad 0 \leq x \leq \frac{\pi}{2}. \]

The sketch of the ordinate set of f(x) = \cos x on [0,\pi/2] is as follows:

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We then compute the volume of the solid of revolution.

    \begin{align*} V = \int_0^{\pi/2} \pi \cos^2 x \, dx &= \frac{\pi}{2} \int_0^{\pi/2} (1 - \cos (2x)) \, dx \\ &= \frac{\pi}{2} \cdot \frac{\pi}{2} \\ &= \frac{\pi^2}{4}. \end{align*}

One comment

  1. 123456grimmjaw says:

    I think that the formula that replaces cosine should have a plus sing instead of the minus sing. It doesn’t matter to the overall result since the integral of cos(2x) is 0….but still, it can cause confusion.

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