Find the volume of revolution when the graph of y=√ x is rotated about the x axis, in the interval [0,1]

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- Apr 18th 2009, 07:49 AMHakhengkimVolume of Revolution
Find the volume of revolution when the graph of y=√ x is rotated about the x axis, in the interval [0,1]

- Apr 18th 2009, 07:59 AMskeeter
- Apr 18th 2009, 08:28 AMHakhengkim
- Apr 18th 2009, 09:05 AMTwig
Itīs worth pointing out that the volume of a thin slice is $\displaystyle y^{2}\cdot \pi \cdot \Delta x $

Since $\displaystyle y = \sqrt{x} \Rightarrow y^{2} = (\sqrt{x})^{2} $

You will get the volume as an integral when you let $\displaystyle \Delta x $ approach zero.

So the formula $\displaystyle \pi \int_{a}^{b} \, y^{2} \, dx $ comes from the volume of a thin slice.