Question

How to tell if an integral is convergent or divergent

Answer 1

Answer:

Convergent - If the limit exists and is a finite number it is a “improper integral convergent” / “convergent”

Divergent - If the limit is positive infinity (+♾️) or doesn’t exist it is a “ improper integral divergent” / “divergent”

Answer 2

To determine if an integral is convergent or divergent, you can use different tests depending on the type of integral. These tests include evaluating definite integrals, using tests for improper integrals, and applying tests for power series.

Step-by-step explanation:

To determine if an integral is convergent or divergent, you can use different tests depending on the type of integral. Here are some common tests:

1. If the integral is a definite integral, you can evaluate it using techniques like substitution, integration by parts, or trigonometric identities. If the integral gives a finite value, then it is convergent. If it gives an infinite value, then it is divergent.
2. If the integral is an improper integral (has limits of integration that are infinite or the function has a discontinuity within the interval of integration), you can use tests like the Comparison Test, Limit Comparison Test, or the Integral Test to check for convergence or divergence.
3. For power series, you can use the Ratio Test, Root Test, or the Direct Comparison Test to determine if the series converges or diverges.

These are just a few of the many tests available. When working with integrals, it's important to consider the properties of the function being integrated and apply the appropriate test to determine convergence or divergence.