What is the Intersection of Two Curves?

In summary, the conversation involves finding the area between two functions, y=x^2-2x and y=x^3. The suggested method is to divide the area into thin rectangles and use integration to find the total area.
  • #1
Jasty
5
0

Homework Statement



y=x^2-2.x
y=x^3

Homework Equations



none

The Attempt at a Solution



I have no idea how to do this so please help me. Thank you.
 
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  • #2
Hi Jasty! :smile:

Are you trying to find the area?

If so, divide it into slices of thickness dx, find the area of each slice, and integrate. :smile:
 
  • #3
1. Draw their graphs.

2. Determine where they intersect.

3. Imagine the area divided into thin, vertical rectangles.

4. What would be the area of each of those rectangles?

5. Their total area is a Riemann sum. Convert that into an integral.
 
  • #4
Thanks a lot. Finally, i found out how to deal with this one.
 

What is a surface made by two curves?

A surface made by two curves is a three-dimensional shape created by the intersection of two curves. These curves can be any type of curve, such as a line, circle, or parabola.

What is the mathematical representation of a surface made by two curves?

The mathematical representation of a surface made by two curves is typically a parametric equation that describes the relationship between two variables and the two curves that form the surface.

What are some real-world examples of surfaces made by two curves?

Some real-world examples of surfaces made by two curves include a saddle, a conical tent, and a seashell. These shapes can be seen in various objects and structures in nature and man-made designs.

What are the properties of a surface made by two curves?

The properties of a surface made by two curves depend on the properties of the two curves that form it. These properties can include curvature, smoothness, symmetry, and intersections with other surfaces.

How are surfaces made by two curves used in mathematics and science?

Surfaces made by two curves have various applications in mathematics and science. They are used to model and analyze physical phenomena, such as fluid flow and electromagnetic fields, and are also studied in geometry and calculus to understand their properties and relationships with other shapes.

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