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July 22, 2014

July 22, 2014

Posted by **Dylan** on Monday, November 28, 2011 at 5:08pm.

Let R be the region between the graph of f and the x-axis on the interval 0 to 1 . Find the volume V of the solid of revolution generated by revolving R about the x-axis. Give both exact (symbolic) and approximate (numeric) answers.

- calculus -
**MathMate**, Monday, November 28, 2011 at 6:21pmConsider a thin vertical slice of width dx.

If we rotate the slice about the x-axis, we get a disk of thinkness dx and area πf(x)^2, so the volume is

πf(x)^2 dx.

Integrate all slices from 0 to 1 gives you

∫πf(x)^2 dx

Hint: I get 0.995... as the volume, and the symbolic answer has a factor of π/3.

If further assistance is required, feel free to post.

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