Chapter 9.4, Problem 34E

To determine

Tostate: whether the integral converges or diverges using the comparison test.

Answer to Problem 34E

The integral is converges.

Explanation of Solution

Given information:

The integral is ${\displaystyle {\int }_{-\infty }^{\infty }\frac{1}{\sqrt{x^4+1}}dx}$ .

using the comparison test, the function of integral can be defined as:

  $0\le \frac{1}{\sqrt{x^4+1}}\le \frac{1}{x^4}$

On the interval $(-\infty \text{,}\infty \text{)}$ and the integral ${\displaystyle {\int }_{-\infty }^{\infty }\frac{1}{x^4}}$ converges,

Thus, the integral isconverges.