Area Between The Curve Problem No 4 - Applications Of Definite Integration - Diploma Maths II

TL;DR

This video explains how to find the area between two parabolas using integration.

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 the curves let us start with problem number 4 find the areas between the parabola Y square is equal to 9 X and X square is equal to 9 Y before drawing these two parabolas the first step that we can do ... Read More

Key Insights

• 👈 The point of intersection of two parabolas is found by setting their equations equal to each other and solving for x or y.
• ❓ Subtracting the areas under the individual parabolas ensures that only the area between the curves is considered.
• 🫡 Integration is used to find the area between the two parabolas by taking the difference of their equations and integrating with respect to x.
• 😥 The limits of integration are determined by the points of intersection of the two parabolas.
• ❎ The final calculated area is given in square units and represents the desired result.
• ❓ The formula for finding the area between the curves is (y1 - y2) dx, where y1 and y2 are the equations of the two parabolas.
• 🥡 The integral of the difference of the two equations is taken with respect to x to find the final area.

Questions & Answers

Q: How do you find the point of intersection of two parabolas?

To find the point of intersection, set the equations of the two parabolas equal to each other. Solve for either x or y, then substitute the obtained value in the other equation to find the corresponding value.

Q: Why do we subtract the areas of the individual parabolas to find the area between them?

Subtracting the areas ensures that we only consider the region between the two curves. If we didn't subtract, we would include the overlapping regions twice in the final area calculation.

Q: What is the formula for finding the required area between two parabolas?

The formula is the integral of (y1 - y2) dx, where y1 represents the equation of one parabola and y2 represents the equation of the other parabola.

Q: How is integration used to calculate the final area?

Integration is used to find the antiderivative of each expression in the formula. The limits of integration are set based on the points of intersection. The result of the integration gives the area between the two parabolas.

Summary & Key Takeaways

• The video provides steps to find the area between two parabolas by first determining their point of intersection.

• The graph of the two parabolas is then plotted, and it is explained that the area between the two curves is found by subtracting the areas formed by each parabola individually.

• The formula for finding the required area is given, and integration is used to calculate the final answer.