What is the Intersection of Two Curves?

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SUMMARY

The discussion focuses on finding the intersection of the curves defined by the equations y=x^2-2x and y=x^3. Participants suggest a methodical approach involving graphing the functions, identifying their intersection points, and calculating the area between them using integration techniques. The area can be approximated by dividing it into thin vertical rectangles, leading to a Riemann sum that can be converted into an integral for precise calculation. This structured method effectively addresses the problem presented.

PREREQUISITES
  • Understanding of polynomial functions and their graphs
  • Knowledge of integration techniques, specifically Riemann sums
  • Familiarity with the concept of intersection points of curves
  • Basic skills in calculus, particularly in setting up and evaluating integrals
NEXT STEPS
  • Learn how to graph polynomial functions using tools like Desmos or GeoGebra
  • Study the method of Riemann sums and its application in definite integrals
  • Explore techniques for finding intersection points of curves analytically
  • Practice solving integration problems involving area between curves
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Students studying calculus, educators teaching integration methods, and anyone interested in understanding the geometric interpretation of integrals and curve intersections.

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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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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:
 
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.
 
Thanks a lot. Finally, i found out how to deal with this one.
 

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