area between the curve problem no 7

TL;DR

This video demonstrates how to find the area bounded by the curves y^2 = 2x and x - y = 4.

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 seven find the area bounded by y square is equal to 2x and the line x minus y is equal to 4 let us find the point of intersection of these two curves from th... Read More

Key Insights

• ❓ The problem involves finding the area bounded by two curves.
• ❣️ Intersection points are calculated by substituting the values of x or y from one equation into the other.
• 🫥 The area is calculated by finding the area under the line and subtracting the area under the parabola.
• ❓ The formula for calculating the area between two curves is the definite integral.
• ❎ The final answer to the problem is 18 square units, representing the area between the curves.
• ❓ Understanding the concepts of integration and solving quadratic equations is essential to solving this problem.
• 😥 Graphing the curves can provide a visual representation of their intersection points and the area between them.

Questions & Answers

Q: How do I find the intersection points between the curves y^2 = 2x and x - y = 4?

To find the intersection points, we can substitute the values of x or y from one equation into the other and solve. By substituting y = 4, we get x = 8, and by substituting y = -2, we get x = 2. Therefore, the intersection points are (8, 4) and (2, -2).

Q: How do I calculate the area between the two curves?

To calculate the area, you need to find the area under the line x - y = 4 and subtract the area under the parabola y^2 = 2x. By using the definite integral, the area can be calculated as the integral of (x + 4) from -2 to 4 minus the integral of (y^2/2) from -2 to 4.

Q: What is the formula used to find the area under a curve?

The formula used to find the area under a curve is the definite integral. For finding the area between two curves, the formula is ∫(upper function - lower function) dx or dy, with the appropriate limits.

Q: What is the final answer to the problem?

The final answer to the problem is 18 square units, which represents the area between the curves y^2 = 2x and x - y = 4.

Summary & Key Takeaways

• The video presents a problem involving finding the intersection points between the curves y^2 = 2x and x - y = 4.

• The intersection points are found to be (8, 4) and (2, -2).

• The video explains how to calculate the area between the two curves by finding the area under the line x - y = 4 and subtracting the area under the parabola y^2 = 2x.