Definite Integral of 1/(1 - x^2) using an Integration Formula with Logarithms | Summary and Q&A

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December 7, 2020
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The Math Sorcerer
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Definite Integral of 1/(1 - x^2) using an Integration Formula with Logarithms

TL;DR

This video explains how to evaluate a definite integral using a formula found in calculus textbooks.

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Questions & Answers

Q: What is the formula used to evaluate the definite integral in the video?

The formula used is the integral of du over one minus u squared, which yields one half times the natural log of the absolute value of one plus u over one minus u, plus a constant of integration.

Q: Why does the video use the formula instead of other methods like partial fractions?

The video specifically chooses to use the formula found in calculus textbooks to demonstrate its application. Other methods like partial fractions could also be used, but the focus here is on using the formula.

Q: How does the video handle the definite integral?

Since it is a definite integral, the video replaces the constant of integration with specific boundary values. In the given example, the boundary values are 5/4 and 2.

Q: Can the formula be applied to other similar definite integrals?

Yes, the formula can be applied to other definite integrals of the same form, where the variable is substituted with the appropriate limits and the expression is evaluated accordingly.

Summary & Key Takeaways

  • The video demonstrates how to evaluate a definite integral using a formula that appears in most calculus books.

  • The formula used in the video involves the integral of du over one minus u squared, and the result is one half times the natural log of the absolute value of one plus u over one minus u, plus a constant of integration.

  • The video provides step-by-step calculations to evaluate a specific definite integral and demonstrates different ways to manipulate the resulting expression.

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