Evaluate the definite integral. $$\int _ { n 2 } ^ { \operatorname { m } 4 } e ^ { - x } d x$$
A) 6
B) $\frac { 1 } { 16 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 1 } { 4 }$
E) 2

Question

Quizplus · Accepted Answer

The integral of e^(-x) is -e^(-x) + C. So, the definite integral from n2 to m4 is -e^(-m4) + e^(-n2). Since n2 is greater than m4, this is equal to e^(-n2) - e^(-m4). Plugging in the values of n and m, we get e^(-4) - e^(-16) = 1/16 - 1/4 = 1/4.

Evaluate the Definite Integral ∫n2m⁡4e−xdx\int _ { n 2 } ^ { \operatorname { m } 4 } e ^ { - x } d x∫n2m4​e−xdx

Evaluate the Definite Integral $\int _ { n 2 } ^ { \operatorname { m } 4 } e ^ { - x } d x$