Integration of Linear and Quadratic Expression problem No. 6 - Integration - Diploma Maths - 2

TL;DR

Solve the problem of integrating the exponential function e^2x upon the square root of a quadratic expression, by converting it into a linear expression.

Transcript

click the bell icon to get latest videos from akira hello friends in this video we are going to see one more problem based on the integration of the form linear expression upon under root of quadratic expression let us start with problem number 6 integral e raise to 2 x upon under root 3 minus 2 e raise to X minus 3 e raise to 2 X DX here you can s... Read More

Key Insights

• 💁 The given problem is not in the form of linear upon the square root of quadratic, which needs to be converted for integration purposes.
• ❓ The exponential function e^2x is substituted as e^x * e^x to simplify the problem.
• 🎮 The integral is solved using substitution and the steps discussed in previous videos.

Questions & Answers

Q: How is the given problem transformed into a linear expression for integration?

The problem is converted by substituting e^2x as e^x * e^x. This allows us to simplify the function and make it solvable.

Q: What are the steps followed to solve the integral?

The steps include substituting the numerator as a into the variability of the denominator plus B, finding the values of A and B, and then separating the integral into two parts.

Q: How is the second part of the integral solved?

The second part, denoted as I1, is solved by using the formula for integrating 1 upon the square root of a quadratic expression.

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

The final answer is -√(3 - 2e^x - 3e^(2x)) - (1/3) √3 sin⁻¹(3e^x + 1/√n) + C, where C represents the constant of integration.

Summary & Key Takeaways

• This video discusses how to solve an integration problem involving an exponential function over a quadratic expression.

• The problem is converted into a linear form by substituting e^2x as e^x * e^x, making it possible to solve.

• The integral is then solved using substitution and the steps described in previous videos.