Question

Find the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the \(x\)-axis.

Hint: You will need to evaluate two integrals. (Assume \(x>0 .\) )

\(y=\frac{1}{x}, y=x_{r}\) and \(y=3 x\)

By computing the volume of the solid obtained by revolving the region under the semicircle \(y=\sqrt{r^{2}-x^{2}}\) from \(x=-r\) to \(x=r\) about the \(x\)-axis, show that the volume of a sphere of radius \(r\) is \(\frac{4}{3} \pi r^{3}\), cublc units. (Do this by setting up the integral.)

Answer 1

As x>0