Integrals of the form Type A Problem No 6 - Integration - Diploma Maths - 2 | Summary and Q&A

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April 12, 2022
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Integrals of the form Type A Problem No 6 - Integration - Diploma Maths - 2

TL;DR

Learn how to solve the integral ∫dx/(1 - sin(2x) - 2cos(2x)) using the substitution method.

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Questions & Answers

Q: What is the integral problem discussed in the video?

The integral problem discussed in the video is ∫dx/(1 - sin(2x) - 2cos(2x)).

Q: What substitution method is used to solve the integral?

The substitution method used to solve the integral is the tangent substitution (T substitution).

Q: How is the integral simplified after the substitution is made?

After the substitution is made, the integral is simplified by finding a common denominator and simplifying the fractions.

Q: What is the final answer to the integral problem?

The final answer to the integral problem is 1/4 ln|3tan(x) - 4/3tan(x) + 1| + C.

Summary & Key Takeaways

  • The video explains how to solve a specific integral problem using the substitution method.

  • The problem involves finding the integral of 1/(1 - sin(2x) - 2cos(2x)).

  • The video demonstrates the step-by-step process of substituting variables and simplifying fractions to solve the integral.

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