Chapter 6.3, Problem 36P

To determine

(a)

To graph the function $f\left(x\right)=e^{-x^2}$ and shade the area represented by the improper integral ${\displaystyle \underset{-\infty }{\overset{\infty }{\int }}{e}^{-x^2}dx}$

To determine

(b)

To find ${\displaystyle \underset{-a}{\overset{a}{\int }}{e}^{-x^2}dx}$ for $a=1,2,3,5$.

To determine

(c)

Show that ${\displaystyle \underset{-\infty }{\overset{\infty }{\int }}{e}^{-x^2}dx}$ converges to finite value.