Evaluate the improper integral or state that it is divergent.
-$$\int _ { 0 } ^ { \infty } 21 e ^ { - 21 x } d x$$
A) Divergent
B) 1
C) 0
D) -1

Question

Quizplus · Accepted Answer

This improper integral converges to 1. It can be evaluated using the formula for the integral of exponential functions, which is $\int_0^{\infty} e^{-ax} dx = \frac{1}{a}$ for $a>0$. Applying this formula with $a=21$, we get $\int_0^{\infty} 21 e^{-21x} dx = \frac{1}{21}$. Therefore, the value of the improper integral is 1.

Evaluate the Improper Integral or State That It Is Divergent ∫0∞21e−21xdx\int _ { 0 } ^ { \infty } 21 e ^ { - 21 x } d x∫0∞​21e−21xdx

Evaluate the Improper Integral or State That It Is Divergent $\int _ { 0 } ^ { \infty } 21 e ^ { - 21 x } d x$