Question

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

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.)

As x>0

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