Chapter 16.4, Problem 40E

(a)

To determine

To approximate: The definite integral ${\displaystyle \underset{0}{\overset{b}{\int }}{e}^{-x^2}}dx$ using calculator for $b=1,5,10\text{and 20}$.

(b)

To determine

Whether the integral ${\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-x^2}}dx$ based on part (a) is convergent or divergent.

(c)

To determine

To explain: Why theintegral ${\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-x^2}}dx$ is convergentwhen comparing with $e^{-x}$ for $x>1$.