Area Between The Curve Problem No 9 - Applications Of Definite Integration - Diploma Maths II

TL;DR

This video discusses how to find the area bounded by two parabolas, using the example of y^2 = x and x^2 = y.

Transcript

click the Bell icon to get latest videos from Ekeeda Hello friends in this video we are going to see one more problem which is based on area between two curves let us start with problem number 9 find the area bounded by the curve y square is equal to X and X square is equal to Y again we have two parabolas right so we can directly draw the graph bu... Read More

Key Insights

• ❓ The problem involves finding the area between two parabolas.
• 😥 The points of intersection between the parabolas are determined by solving the equations simultaneously.
• 📈 Drawing the graphs helps visualize the common region.
• ❓ The area is found by subtracting the integral of one curve from the integral of the other.
• 😘 Substituting the upper and lower limits into the integrals gives the final answer.
• ❎ The area is given in square units.
• 🌍 The solution demonstrates the application of calculus concepts to real-world problems.

Questions & Answers

Q: What are the equations of the two parabolas discussed in the video?

The two parabolas are y^2 = x and x^2 = y.

Q: How can the points of intersection between the two parabolas be found?

By substituting one equation into the other and simplifying, we can find the values of x that satisfy both equations, giving us the points of intersection.

Q: What is the method used to find the area between the two curves?

The area is found by subtracting the integral of one curve from the integral of the other, both within the limits of the points of intersection.

Q: What is the final answer for the area between the curves in this example?

The final answer is 1/3 square units.

Summary & Key Takeaways

• The video demonstrates how to find the points of intersection between the two parabolas y^2 = x and x^2 = y.

• It explains how to draw the graphs of the parabolas and determine their common region.

• The method of finding the area between the two curves is explained using integrals and limits.