Determine whether the integral converges or diverges. Find the value of the integral if it converges.
A) The integral diverges.
B) The integral evaluates to .
C) The integral evaluates to .
D) The integral evaluates to .

Question

Determine whether the integral converges or diverges. Find the value of the integral if it converges. 
A) The integral diverges. 
B) The integral evaluates to . 
C) The integral evaluates to . 
D) The integral evaluates to .

Quizplus · Accepted Answer

The integral cannot be evaluated without additional information, but we can use the divergence test to determine that the integral diverges. The divergence test states that if the limit of the integrand as x approaches infinity (or negative infinity) does not equal zero, then the integral diverges. In this case, the limit of e^x/sqrt(x) as x approaches infinity is infinity, so the integral diverges.

Determine Whether the Integral Converges or Diverges