Evaluate $\int _ { 1 } ^ { \infty } e ^ { - 5 x } d x$ .
A) $\frac { 1 } { 5 e ^ { 5 } }$
B) $\frac { 1 } { 5 e }$
C) $e ^ { 5 }$
D) $5 e ^ { 5 }$

Question

Quizplus · Accepted Answer

The integral of $e^{-5x}$ from 1 to $\infty$ is evaluated using the formula for the integral of an exponential function, $\int e^{ax} dx = \frac{1}{a}e^{ax} + C$. Applying this to the given integral, we get $\int _ { 1 } ^ { \infty } e ^ { - 5 x } d x = \left[ \frac{-1}{5}e^{-5x} \right]_1^\infty = 0 - \left( \frac{-1}{5}e^{-5} \right) = \frac{1}{5e^5}$.

Evaluate ∫1∞e−5xdx\int _ { 1 } ^ { \infty } e ^ { - 5 x } d x∫1∞​e−5xdx

Evaluate $\int _ { 1 } ^ { \infty } e ^ { - 5 x } d x$