Question

Improper Integral (Integrals with Infinite Limits)

∫e^x dx from - ∞ to 1

Answer 1

Given Improper integral is-

$I=\int_{-\infty}^1e^xdx$

So, This integral can be written as-

$I=lim_{p\to \infty}\int_-p^1e^xdx \\ =lim_{p\to \infty}e^x|_p^1 \\ =lim_{p\to \infty} (e-e^{-p})\\$

$=e-\dfrac{1}{e^{\infty}} =e-\dfrac{1}{\infty}=e-0=e$