Problem no 20 on beta function - Beta and Gamma Function - Engineering Mathematics - 2

TL;DR

The video explains the method of proving the property of the Beta and Gamma function using a specific integration.

Transcript

hi guys so here i have question for you and it is based on the beta and gamma function so the given term is integration 0 to infinity x raised to p minus 1 upon 1 plus x dx is equal to pi upon sine p pi so the value of the integration is given and we have to prove that gamma p into gamma 1 minus p is equal to pi upon sine now guys let me tell you t... Read More

Key Insights

• 🤨 The property of gamma p multiplied by gamma 1 minus p being equal to pi upon sine p pi is an important result in the study of the Beta and Gamma function.
• 😇 The substitution x = tan square theta is commonly used when evaluating integrals with limits from zero to infinity.
• ❓ The definition of the Beta function is used to simplify the integration and obtain the final result.
• 👍 Proving mathematical properties and formulas requires careful manipulation of equations and the application of known mathematical concepts.
• ❓ The relationship between the Beta and Gamma function is utilized in the proof to derive the desired result.
• 👍 The property being proved in the video can be used to solve various numerical problems involving the Beta and Gamma function.
• 🔨 The concept of substitution in integration is a powerful tool that can simplify complex integrals.

Questions & Answers

Q: What is the property of the Beta and Gamma function that is being demonstrated in the video?

The property states that gamma p multiplied by gamma 1 minus p is equal to pi upon sine p pi.

Q: How is the given integration evaluated?

The integration is evaluated by substituting x = tan square theta and converting the function into sine and cosine using trigonometric identities.

Q: How is the property of the Beta and Gamma function used in the proof?

The property is used in the final step of the proof to equate the value obtained from the integration with the given value of pi upon sine p pi.

Q: Where can I find more videos on the Beta and Gamma function and other topics in engineering mathematics?

You can find more videos on the Beta and Gamma function, as well as other topics in engineering mathematics, on the website ekita.com.

Summary & Key Takeaways

• The video discusses the property of the Beta and Gamma function and demonstrates the method of proving it using a given integration.

• The property states that gamma p multiplied by gamma 1 minus p is equal to pi upon sine p pi.

• The video explains the concept of substitution and uses the substitution x = tan square theta to evaluate the integration.