# How do you show whether the improper integral #int (x^2)/(9+x^6) dx# converges or diverges from negative infinity to infinity?

Refer to explanation

Let's calculate the indefinite integral hence we have

Hence the definite is

So we have that

Hence the integral converges.

By signing up, you agree to our Terms of Service and Privacy Policy

To determine whether the improper integral ( \int_{-\infty}^{\infty} \frac{x^2}{9+x^6} , dx ) converges or diverges, follow these steps:

- Check for Symmetry: Observe if the integrand is an even or odd function.
- Find Vertical Asymptotes: Identify any vertical asymptotes by setting the denominator equal to zero and solving for ( x ).
- Use Comparison Test: Compare the integrand with a known function whose convergence or divergence is known.
- Evaluate Limits: Split the integral into two parts and evaluate each limit separately.

By analyzing these factors, you can determine whether the given improper integral converges or diverges.

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you use the ratio test to test the convergence of the series #∑ 11^n/((n+1)(7^(2n+1)))# from n=1 to infinity?
- How do you use the Comparison Test to see if #1/(4n^2-1)# converges, n is going to infinity?
- What is the difference between an infinite sequence and an infinite series?
- Using the integral test, how do you show whether #sum 1 / [sqrt(n) * (sqrt(n) + 1)]# diverges or converges from n=1 to infinity?
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))+...#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7