Integration Using Two Important Results Problem No 5 - Integration - Diploma Maths - II

TL;DR

Learn how to solve an integral problem using important results from the previous video.

Transcript

click the bell icon to get latest videos from Ekeeda Hello friends in this video we are going to solve problem number five which are based on two important results that we have seen in the previous video let us start with it integral sin 2x upon under root a square sin square X plus B square cos square X DX here we are going to use the second impor... Read More

Key Insights

• 🎮 Important results from previous videos are used to solve the integral problem.
• 🫚 The derivative of the function inside the square root is sin(2x).
• 🍉 The constant is adjusted to eliminate unwanted terms in the numerator.

Questions & Answers

Q: What equation is used to solve the integral sin^2x/√(a^2sin^2x + b^2cos^2x)?

The equation used is integration of f'(x)/√f(x) = 2√f(x) + C.

Q: How is the derivative of the function inside the square root determined?

By differentiating the function, we get sin(2x).

Q: How is the constant adjusted to eliminate a term in the numerator?

By assuming a^2sin^2x + b^2cos^2x as a variable T and differentiating with respect to T, we can transfer a^2 - b^2 to the denominator.

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

The final solution is 2√(a^2sin^2x + b^2cos^2x)/(a^2 - b^2) + C.

Summary & Key Takeaways

• The video explains the integration of sin^2x/√(a^2sin^2x + b^2cos^2x) using a previously discussed result.

• The derivative of the function inside the square root is shown to be sin(2x).

• By substituting variables and using integration formulas, the final solution is found to be 2√(a^2sin^2x + b^2cos^2x)/(a^2 - b^2) + C.