Area Between The Curve Problem No 8 - Applications Of Definite Integration - Diploma Maths II

TL;DR

Find the area between a parabola and a chord, equal to 16/3 square units.

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 eight two points a 1 comma 4 and B 9 gamma 12 are on the parabola Y square is equal to 16x show that the area enclosed between the chord A B and the parabola... Read More

Key Insights

• ❓ Problem involves determining area between curves using integration.
• ❓ Equations of parabola and chord essential to calculate enclosed area.
• ❓ Integration techniques applied to find total area and subtract portions.
• 🪡 Understanding of geometry and calculus principles needed to solve problem.
• 😥 Limits of integration determined by points A and B on the curves.
• ❓ Final result confirms the area enclosed between parabola and chord.
• 😑 Mathematical expressions and substitutions crucial in solving the problem.

Questions & Answers

Q: What is the equation of the parabola in the given problem?

The equation of the parabola is Y^2=16X in the problem where two points A and B lie on it.

Q: How is the equation of the chord AB found?

The equation of chord AB is found using the two-point form with points A(1, 4) and B(9, 12).

Q: How is the area between the parabola and chord calculated?

The area is calculated by integrating the equations of the parabola and chord with respect to the x-axis.

Q: What is the final result of the enclosed area between the parabola and chord?

The final area is computed to be 16/3 square units after integrating the equations and applying the limits.

Summary & Key Takeaways

• Problem involves finding area between parabola Y^2=16X and chord AB.

• Equations of parabola and chord calculated to determine enclosed area.

• Integration of equations leads to area of 16/3 square units.