Definite Integration Based on Property No 4 Problem No 5

TL;DR

The video explains how to apply the fourth property of definite integrals to solve a specific problem.

Transcript

click the Bell icon to get latest videos from equator hello friends in this video we are going to see one more problem which is based on property number four of definite integral so let us start with problem number five integral minus 5 by 2 to plus 5 by 2 sine square X upon sine square X plus cos square X DX so first considering the given function... Read More

Key Insights

• 🦕 The video explains the concept of even and odd functions and applies it to the given function.
• ⛔ It demonstrates the property of even functions in splitting the integral limits.
• 🍉 The video highlights the cancellation of terms in adding the two integrals.

Questions & Answers

Q: What is the problem being discussed in the video?

The problem is to evaluate the integral of sin^2(x) / [sin^2(x) + cos^2(x)] from -5/2 to 5/2.

Q: How is it determined that the given function is an even function?

By substituting -x for x in the function and observing that the resulting function is equal to the original function.

Q: What is the property used to split the integral in the problem?

The property states that if a function is even, the integral from 0 to a can be written as twice the integral from 0 to a/2.

Q: What is the final answer to the problem?

The final answer is PI/2.

Summary & Key Takeaways

• The video discusses a problem involving the integral of sin^2(x) / [sin^2(x) + cos^2(x)] from -5/2 to 5/2.

• It demonstrates that the given function is an even function.

• It applies the property of even functions to split the integral and solve the problem.