Definite Integration Problem No 12 - Definite Integration - Diploma Maths II

TL;DR

This video solves an integral problem using property number one, demonstrating how to manipulate and simplify the equation.

Transcript

click the bell icon to get latest videos from Ikeda hello friends in this video we are going to continue one more problem based on property number one of definite integral let us start with problem number 12 integral PI by six to PI by 3 1 upon 1 plus cot X DX considering this given function as equation number 1 in the next step we can use the prop... Read More

Key Insights

• 👻 Property number one of definite integrals allows for manipulation and simplification of equations.
• 🆘 The conversion of trigonometric functions can help make the equation more manageable.
• 😑 Combining fractions with the same denominator simplifies the expression.

Questions & Answers

Q: What property of definite integrals is used in the video?

The video uses property number one, which states that the integral from A to B of f(X) dX is equal to the integral from A to B of f(a+b-X) dX.

Q: How are cotX and tanX converted to sine and cosine?

The video uses the interrelation formula of trigonometry, which states that cotX can be written as cosX/sinX and tanX can be written as sinX/cosX.

Q: How are the two fractions in the denominator simplified?

The video combines the two fractions by keeping the denominator the same, resulting in the simplified expression of (sinX + cosX)/(sinX + cosX), which cancels out.

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

The final answer is I = PI/12.

Summary & Key Takeaways

• The video addresses problem number 12, solving the integral of 1/(1+cotX) from PI/6 to PI/3 using property number one of definite integrals.

• By replacing X with the lower limit plus the upper limit minus X, the equation is simplified.

• The video also showcases the use of complementary angle formula and the conversion of cotX and tanX to sine and cosine.