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