Determine whether the improper integral converges or diverges.
-$$\int _ { 1 } ^ { \infty } \frac { e ^ { x } } { \sqrt { 1 + x ^ { 2 } } } d x$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

The integral diverges because the exponential function $e^x$ grows much faster than the denominator $\sqrt{1+x^2}$ as $x$ approaches infinity, causing the integral to increase without bound.

Determine Whether the Improper Integral Converges or Diverges ∫1∞ex1+x2dx\int _ { 1 } ^ { \infty } \frac { e ^ { x } } { \sqrt { 1 + x ^ { 2 } } } d x∫1∞​1+x2​ex​dx

Determine Whether the Improper Integral Converges or Diverges $\int _ { 1 } ^ { \infty } \frac { e ^ { x } } { \sqrt { 1 + x ^ { 2 } } } d x$