Evaluate $\int _ { 1 } ^ { \infty } e ^ { - 7 x } d x$ . A) $\frac { 1 } { 7 e ^ { 7 } }$ B) $\frac { 1 } { 7 e }$ C) e⁷ D) $7 e ^ { 7 }$

Question

Quizplus · Accepted Answer

The integral $\int e^{-7x} dx$ evaluates to $-\frac{1}{7}e^{-7x} + C$. Applying the limits from 1 to $\infty$, we get $\lim_{x \to \infty} (-\frac{1}{7}e^{-7x}) - (-\frac{1}{7}e^{-7*1}) = 0 - (-\frac{1}{7}e^{-7}) = \frac{1}{7e^7}$.

Evaluate ∫1∞e−7xdx\int _ { 1 } ^ { \infty } e ^ { - 7 x } d x∫1∞​e−7xdx

Evaluate $\int _ { 1 } ^ { \infty } e ^ { - 7 x } d x$