Integration of Composite Functions Problem No 3 - Integration - Diploma Maths - II | Summary and Q&A

TL;DR

Learn how to find the integration of a composite function with a fractional power in this video.

Key Insights

• ✊ The function in the problem is a composite function with a fractional power in the denominator.
• 💁 To find the integration, the function is converted to a form that can be compared with the standard integration formula.
• ✊ The integration is found using the formula for integration of X raised to a fractional power.
• 😑 The derivative of the replacing function is used in the final integration to simplify the expression.

Transcript

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Questions & Answers

Q: What is a composite function?

A composite function is a function that has another function inside its definition. In this case, the function has a fractional power in the denominator.

Q: How is the function converted to a form that can be compared with X raised to n?

The function is rewritten as 4/(2 - 3x)^(3/4). The fourth root is changed to exponent form, and the cube is moved to the denominator.

Q: What is the formula for integration of X raised to n?

The formula is X^(n+1)/(n+1), where n is the power raised to X. In this case, n is -3/4.

Q: How is the derivative of the function used in the final integration?

The derivative of the function inside the composite function is divided by the derivative of the replacing function (2 - 3x). This step helps in simplifying the integration.

Summary & Key Takeaways

• The video discusses how to find the integration of the function 4/(4th root of 2 - 3x)^3.

• The function is a composite function with a fractional power in the denominator.

• The function is converted to a form that can be compared with the standard function for integration of X raised to n.

• The integration is found using the formula for integration of X raised to n.