Question

${\int }_0^{\infty }{e}^{-x}dx=$.

• A. 0.0
• B. 1
• C. $\infty$
• D. 2

Answer 1

The correct option is B 1

We can see that the given integral is an improper integral as one of its limits is not finite.
In such cases where we have to deal with infinity as the limits of definite integral.
${\int }_0^{\infty }{e}^{-x}dx.=lima\to \infty {\int }_0^a{e}^{-x}dx$
$=lima\to \infty (-e^{-x}{)}_0^a$
$=lima\to \infty (-e^{-a}-(-e^0\left)\right)$
$=0-(-1)$
$=1$