Definite Integration problem no 3  Definite Integration  Diploma Maths  2  Summary and Q&A
TL;DR
This video explains how to solve a specific definite integration problem stepbystep.
Questions & Answers
Q: How is the definite integral of 2/(2x + 3) solved in this video?
The integral is transformed by substituting 2x + 3 for x, using the derivative of 2x + 3 to divide the integral, and then substituting the limits of integration.
Q: What is the final answer to the definite integral in this problem?
The final answer is (1/2) log(11/7).
Q: Why is the derivative of 2x + 3 divided by the original function in the integration process?
Dividing by the derivative simplifies the integral by canceling out the substitution. It allows us to solve the integral of 1/x and then multiply it by the derivative.
Q: How are the limits of integration substituted in the final step?
The upper limit of 4 is replaced with 2(4) + 3 in the log expression, and the lower limit of 2 is replaced with 2(2) + 3. These values are then used to calculate the final result.
Summary & Key Takeaways

The video discusses solving the definite integral of 2/(2x + 3) from 2 to 4 using a substitution method.

By comparing the integral to the integral of 1/x, the composite function 2x + 3 is used as a substitution.

The derivative of 2x + 3 is divided by the original function to simplify the integral, and the limits are substituted accordingly.