Area of a triangle w/calculus?

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SUMMARY

The discussion focuses on calculating the area of a triangle with vertices at (0,0), (5,2), and (-1,6) using calculus. Participants emphasize the importance of graphing the triangle to determine the appropriate line for integration. They recommend using integration techniques and suggest exploring cross products for a deeper understanding of area calculations. A specific resource is provided for further guidance on using cross products to find the area of a parallelogram, which can be adapted for triangles.

PREREQUISITES
  • Understanding of calculus concepts, specifically integration
  • Familiarity with graphing techniques for geometric shapes
  • Knowledge of cross products in vector calculus
  • Basic geometry principles related to triangles
NEXT STEPS
  • Explore integration techniques for calculating areas under curves
  • Learn about vector cross products and their application in area calculations
  • Study the method of using determinants to find the area of polygons
  • Investigate graphical methods for visualizing geometric shapes and their areas
USEFUL FOR

Students studying calculus, educators teaching geometry, and anyone interested in applying calculus to solve geometric problems.

SciSteve
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consider a triangle with the given vertices. (0,0), (5,2), (-1,6) Use calculus to find the area of the triangle.
Not quite sure how to do this..
 
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draw the graph and think about which line you want the area under and from which limits (you definitely need to integrate)
 

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