Chapter 8.1, Problem 87E

(a)

To determine

To calculate: The volume of the solid generated when the region bounded by the curve, $y=e^{-x^2},y=0,x=0$ and $x=b,\left(b>0\right)$ is revolved about the y-axis for $b=1$.

(b)

To determine

To calculate: The value of b such that the volume generated the when the region bounded by the curve, $y=e^{-x^2},y=0,x=0$ and $x=b,\left(b>0\right)$ is revolved about the y-axis is $\frac{4}{3}\text{cubic units}$.