Definite Integration problem no 3 - Definite Integration - Diploma Maths - 2 | Summary and Q&A

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June 13, 2019
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Definite Integration problem no 3 - Definite Integration - Diploma Maths - 2

TL;DR

This video explains how to solve a specific definite integration problem step-by-step.

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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.

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