Integration of Composite Functions Problem No 5 - Integration - Diploma Maths - II

TL;DR

Learn how to evaluate the integral of (1/(cube root of (1 - 3x)^2)) and simplify it step by step.

Transcript

click the Bell icon to get latest videos from equator hello friends in this video we are going to solve a one more problem on integration of composite function let us start with problem number five evaluate integral DX upon cube root of 1 minus 3x the whole square now in this case I can compare this function with X raised to n but before that I nee... Read More

Key Insights

• 🫚 The given function is simplified by converting the cube root into a fraction.
• 📫 Integration of composite functions involves comparing the function to X raised to n.
• ✊ The power rule is applied to evaluate the integral of the function.
• 😑 The resulting expression is simplified to obtain the final integration result.
• 🍉 Converting terms into fractions can make it easier to apply integration techniques.
• 📏 The derivative of a composite function is found by applying the chain rule.
• ✊ The power rule is a fundamental concept in evaluating integrals.

Questions & Answers

Q: How is the given function simplified by converting the cube root term?

The cube root term is converted into a fraction, resulting in (1/(1 - 3x)^(2/3)).

Q: How is the function compared to X raised to n for integration?

The function is compared to X raised to n by replacing X with (1 - 3x) and finding its derivative.

Q: What is the derivative of (1 - 3x) in the context of integration?

The derivative of (1 - 3x) is -3, as the derivative of X is 1.

Q: How is the integral of the function evaluated?

The integral is evaluated using the power rule by raising the function to (1/3) and simplifying the resulting expression.

Summary & Key Takeaways

• The video explains how to simplify the given function by converting the cube root term into a fraction.

• The function is then compared to X raised to n so that integration can be carried out.

• The integral is evaluated by applying the power rule and simplifying the resulting expression.