Chapter 6.3, Problem 34P

To determine

(a)

To find ${\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-2t}dt}$ for $b=3,5,7,10$ and give your observation about convergence of the integral.

To determine

(b)

To find the value of ${\displaystyle \underset{0}{\overset{b}{\int }}{e}^{-2t}dt}$ using Fundamental theorem of calculus.

To determine

(c)

To find the value of ${\displaystyle \underset{0}{\overset{b}{\int }}{e}^{-2t}dt}$ using Fundamental theorem of calculus at $b\to \infty$.