How could I evaluate this IMPROPER integra?

Thread starter frasifrasi
Start date Nov 3, 2007

In summary, an integral is considered improper if the limits of integration are infinite or the function being integrated is undefined at a point within the limits of integration. A proper integral has finite limits of integration and a continuous function, while an improper integral has infinite limits or a non-continuous function. To evaluate an improper integral, you can use the limit definition or other common techniques such as splitting the integral or using integration by parts. To determine convergence or divergence, you can analyze the limit of the integral or the behavior of the function near points of discontinuity.

Nov 3, 2007

frasifrasi

Int from 1 to infinity of ln(X)/x^(3)

--> Any ideas on how to get started(mainly the technique)? thank you.

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Nov 3, 2007

Dick

Science Advisor

Homework Helper

You would first find an indefinite integral using integration by parts.

Nov 4, 2007

benjyk

Let u = ln x and dv/dx = x^-3 and use integration by parts.
And see what happens as the upper bound of the integral tends to infinity.

1. How do I know if an integral is improper?

An integral is considered improper if one or both of the following conditions are met: the limits of integration are infinite or the function being integrated is undefined at a point within the limits of integration.

2. What is the difference between a proper and an improper integral?

A proper integral has finite limits of integration and the function being integrated is continuous within those limits. An improper integral, on the other hand, has infinite limits of integration or the function is not continuous within the limits.

3. How can I evaluate an improper integral?

To evaluate an improper integral, you can use the limit definition of the integral. This involves taking the limit of the integral as one or both of the limits of integration approaches infinity or a point where the function is undefined.

4. What are some common techniques for evaluating improper integrals?

The most common techniques for evaluating improper integrals include using the limit definition of the integral, splitting the integral into two or more proper integrals, and using integration by parts.

5. What are some tips for determining whether an improper integral converges or diverges?

If the integral has infinite limits of integration, you can evaluate the limit as the limits of integration approach infinity. If the limit is finite, the integral converges. If the limit is infinite, the integral diverges. If the function being integrated is undefined within the limits of integration, you can analyze the behavior of the function near the point of discontinuity to determine convergence or divergence.