Help me cut the area under a parabola in half

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    Area Cut Parabola
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SUMMARY

The discussion focuses on determining the equation of a line through the origin that bisects the area under the curve defined by the function f(x) = 2x - x², which is situated above the x-axis. The area under this parabola can be calculated using definite integrals, and the goal is to find a line that divides this area into two equal sections. Participants are encouraged to share their progress and seek guidance as needed.

PREREQUISITES
  • Understanding of definite integrals in calculus
  • Familiarity with the properties of parabolic functions
  • Knowledge of how to find the area under a curve
  • Ability to derive equations of lines from given points
NEXT STEPS
  • Study the process of calculating definite integrals for parabolic functions
  • Learn how to derive the equation of a line from two points
  • Explore methods for finding the centroid of a region bounded by curves
  • Investigate techniques for solving optimization problems in calculus
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in solving optimization problems related to areas under curves.

Tennisgoalie
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The problem is: Consider the area under the curve f(x)=2x-x2 and above the x axis. Find the equation of the line through the origin that cuts this area into two equal parts.
 
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Here is a link to a very similar problem, and from this you may see how to work this problem:

http://mathhelpboards.com/questions-other-sites-52/phyllis-question-yahoo-answers-regarding-finding-line-divides-area-into-equal-parts-7197.html

Now, please feel free to post your progress using the above as a guide if you get stuck, and we will be glad to offer further guidance. :D
 

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