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

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- November 1st 2008, 10:32 AMwhocares27A 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 - November 1st 2008, 10:54 AMShyam
- November 2nd 2008, 09:58 AMwhocares27
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

- November 2nd 2008, 04:39 PMqorilla
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) - November 2nd 2008, 07:03 PMwhocares27
thank you very much

- November 2nd 2008, 07:12 PMShyam
Hello Gorilla,

Which software do you use to draw graphs??? Where can I get that software??? - November 2nd 2008, 11:58 PMqorilla
Hi Shyam!

WZgrapher:

WZGrapher Function Grapher