Chapter B.1, Problem 3P

(a)

To determine

To Evaluate: ${\displaystyle \underset{-\infty }{\overset{\infty }{\int }}x{e}^{-a{x}^2}dx}$ .

(b)

To determine

To Evaluate:Indefinite integral of $x{e}^{-a{x}^2}$ .

(c)

To determine

The evaluation of ${\displaystyle \underset{0}{\overset{\infty }{\int }}x{e}^{-a{x}^2}dx}$ .

(d)

To determine

To Evaluate: ${\displaystyle \underset{0}{\overset{\infty }{\int }}x{e}^{-a{x}^2}dx}$ by differentiating the previous result.