Question

The volume of solid obtained by revolving the region between the graph $f\left(x\right)=\sqrt{x}\text{and}g\left(x\right)=x^3\text{on}[0,1]$around (a)the y axis (b)the line x=2

Short answer

Part (a) The solid of revolution has a volume of $\frac{2}{5}\pi$

Part (b) The solid of revolution has a volume of $\frac{19}{15}\pi$

Step-by-step solution

Part (a) Step 1. Given information 

We have been given to find out the volume covered by the region between the given graphs .

$f\left(x\right)=\sqrt{x}\text{and}g\left(x\right)=x^3\text{on}[0,1]$

Part (a) Step 2.Showing problem through graph 

a

Part (a) Step 3.

a