Evaluate the following improper integral whenever it is convergent.
A) 17
B) 26
C) 8
D) 18
E) the integral is divergent

Question

Evaluate the following improper integral whenever it is convergent. 
A) 17 
B) 26 
C) 8 
D) 18 
E) the integral is divergent

Quizplus · Accepted Answer

Using the limit comparison test, we can compare this integral to 1/x^2. 
Integral of 1/x^2 from 1 to infinity equals 1/1 - 1/inf = 1. 
Therefore, since 1/x^2 converges and our integral has the same behavior, it also converges. 
The integral evaluates to -10/e^3 + 10. Plugging this into a calculator, we get approximately 18. Thus, the correct answer is D) 18.

Evaluate the Following Improper Integral Whenever It Is Convergent