MHB Help me cut the area under a parabola in half

[Tennisgoalie]

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.

 

[MarkFL]

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