Evaluate the following improper integral whenever it is convergent.
A)4
B)-1
C)1
D)7
E)the integral is divergent

Question

Evaluate the following improper integral whenever it is convergent. 
A)4 
B)-1 
C)1 
D)7 
E)the integral is divergent

Quizplus · Accepted Answer

The given improper integral is of the form $\int_{a}^{\infty}f(x)dx$, where $f(x) = \frac{2}{x^2+1}$. This integral is divergent because the function $f(x)$ does not approach $0$ as $x$ approaches $\infty$. We can see this by noticing that $f(x) \geq \frac{2}{x^2+4} \implies \lim_{x 	o \infty}f(x) \geq \lim_{x 	o \infty}\frac{2}{x^2+4} = 0$. Hence, the given improper integral is divergent.

Evaluate the Following Improper Integral Whenever It Is Convergent