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

TL;DR

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

Key Insights

• 🎮 The video explains the step-by-step process of solving a specific integral problem.
• ❓ The substitution method, specifically the tangent substitution, is used to simplify the integral.
• ❓ Finding a common denominator and simplifying fractions are important steps in solving the integral.

Transcript

click the bell icon to get latest videos from equator hello friends in this video we are going to see a last problem which is based on integral one upon a sine 2x plus B cos 2 X plus C let us start with problem number 6 is given as integral DX upon 1 minus sine 2x minus 2 cos 2 X 4 that we know now that the substitution is panics SD for that the va... Read More

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.