Type 2 Problems Part 2 Problem No 2 - Definite Integration - Diploma Maths II

TL;DR

Property number 2 states that the integral of f(x) from 0 to a is equal to the integral of f(a - x) from 0 to a.

Transcript

click the Bell icon to get latest videos from Ekeeda Hello friends in this video we are going to see new topic that is problems based on property number 2 now what is property number 2 it says integral 0 to a f of X DX is equal to integral 0 to a F of a minus X DX now let us see how to identify this problem in the given integral you can see the low... Read More

Key Insights

• ☺️ Property number 2 in integrals allows us to simplify certain integrals by replacing the variable with (a - x).
• 😘 It is applicable when the lower limit of the integral is 0.
• 💁 By applying property number 2, we can transform an integral with a complex function into a simpler form.
• 🪜 Adding two integrals with the same denominator can be simplified by canceling out the numerator and keeping the common denominator.

Questions & Answers

Q: What is property number 2 in integrals?

Property number 2 states that the integral of a function from 0 to a is equal to the integral of the same function with the variable replaced by (a - x) from 0 to a. It allows us to simplify certain integrals.

Q: How do you identify a problem where property number 2 can be applied?

To identify a problem where property number 2 can be applied, check if the lower limit of the integral is 0. If it is, then property number 2 can be used to simplify the integral.

Q: Can you provide an example problem and demonstrate how to solve it using property number 2?

Yes, for example, let's consider the integral from 0 to a of root(x) / (root(x) + root(a - x)). By applying property number 2, we can rewrite it as the integral from 0 to a of root(a - x) / (root(a - x) + root(x)).

Q: What is the final answer obtained by solving the example problem using property number 2?

By solving the example problem using property number 2, the final answer is obtained as the value of a divided by 2.

Summary & Key Takeaways

• The video discusses problems based on property number 2 in integrals.

• Property number 2 states that the integral of a function from 0 to a is equal to the integral of the same function with the variable replaced by (a - x) from 0 to a.

• The video provides an example problem and demonstrates how to apply property number 2 to solve it.