Integration of Linear and Quadratic Expression problem NO 1 - Integration - Diploma Maths - 2

TL;DR

This video explains how to find the integral of linear equations divided by quadratic equations using a substitution method.

Transcript

click the bell icon to get latest videos from akira hello friends in this video we are going to see a new form of integration that is integral of the form linear upon quadratic let us start with problem number 1 integral X upon X square plus 3x minus 4 DX now remember friends in the previous videos we have seen how to find the integration of 1 upon... Read More

Key Insights

• 👶 The video explains a new form of integration involving linear upon quadratic equations.
• ⌛ The process involves writing the numerator as a times the derivative of the denominator plus B.
• 😃 The values of a and B can be determined by comparing coefficients.
• 🥳 The integral is then split into two parts: one involving the derivative of the denominator and the other as a quadratic.
• 🍉 The integral of 1 upon quadratic equations can be solved using the third-term method.

Questions & Answers

Q: How can the integral of linear upon quadratic equations be solved using the substitution method?

To solve such integrals, the numerator is written as a times the derivative of the denominator plus B. By comparing coefficients, the values of a and B are determined, and the integral is split into two parts: one with the derivative of the denominator and the other as a quadratic.

Q: What is the step-by-step process for finding the integral of linear upon quadratic equations?

The first step is to write the numerator as a times the derivative of the denominator plus B. Then, by comparing coefficients, the values of a and B are determined. The integral is then split into two parts: one involving the derivative of the denominator and the other as a quadratic.

Q: How can the integral of 1 upon quadratic equations be solved?

The integral of 1 upon quadratic equations can be solved using the third-term method. By adding and subtracting the third term in the denominator, the equation is simplified. The integral can then be solved using the standard formula for X square minus Y square.

Q: What is the final answer for the given integral of X upon X square plus 3x minus 4 DX?

The final answer for the integral is one-half log of X square plus 3x minus 4 minus three-tenths log of X minus 1 upon X plus 4 plus C.

Summary & Key Takeaways

• The video introduces a new form of integration, specifically integrals of the form linear upon quadratic.

• To solve these integrals, the first step is to write the numerator of the linear equation as a times the denominator plus B times the derivative of the denominator.

• By comparing coefficients, the values of a and B can be determined and substituted back into the equation. The integral is then separated into two parts: one involving the derivative of the denominator and the other involving a quadratic.