Thread: A complicated equal area problem

Let R be the region bounded by the parabola y=x-x^2 and the x axis from 0 to 1

find the equation y=mx that divides this region into two regions of equal area

Originally Posted by whocares27

Let R be the region bounded by the parabola y=x-x^2 and the x axis from 0 to 1

find the equation y=mx that divides this region into two regions of equal area

Please see attached graph, and then try to understand and solve.

i understand what you showed me with x=.5 would bisect it in half, but i need a line that fits the equation y=mx meaning it will have to go through the origin

We want that
Yellow = Green + Red

For a given h, we can calculate the green triangle's area.
By integration from 0 to h, we can get the sum of Yellow and Green.
By integration from h to 1, we find Red.

Using our equation above (Yellow = Green + Red) and these methods for calculating the areas, we can find h.
then m in y=mx can be calculated quickly:

m=(h-h^2)/h=1-h, which is
m= 1 - (cubic root of half)

thank you very much

Hello Gorilla,

Which software do you use to draw graphs??? Where can I get that software???

Hi Shyam!
WZgrapher:

WZGrapher Function Grapher