The integral :
A) diverges since the power of is not less than 1.
B) converges since the power of is greater than 1.
C) diverges since .
D) converges since .
E) none of the above

Question

The integral  :
A) diverges since the power of is not less than 1. 
B) converges since the power of is greater than 1. 
C) diverges since . 
D) converges since . 
E) none of the above

Quizplus · Accepted Answer

The given integral can be rewritten as $\int_{0}^{1} x^{11} e^{x} dx$. As the power of $x$ is greater than 1, the integral diverges by the p-test. Therefore, the correct choice is (A) diverges since the power of $x$ is not less than 1.

The Integral