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A plane curve whose equation is $y - f (x) = 0$ passes through the origin.Consider the rectangle $R_x$ formed by the coordinate axes and lines parallel to the axis passing through the point $(x, f (x))$ of the curve lines. If the curve divides the rectangle into two regions and one of the area of the region is 10 times the area of the other.

How can I find $f$.I stuck in this exercise some help please.

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Area of rectangle : $x\times f(x)$

One part of area: $\int_0^x f(x) dx$.

Can you do it now?

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  • $\begingroup$ but how can i interpret "If the curve divides the rectangle into two regions and one of the area of the region is 10 times the area of the other". $\endgroup$ – Knight May 12 '14 at 16:35
  • $\begingroup$ A curve passes though two opposite vertices of a rectangle and thus dividing it into two parts $\endgroup$ – evil999man May 12 '14 at 16:36
  • $\begingroup$ mmmmm ok i will try again .... $\endgroup$ – Knight May 12 '14 at 16:37
  • $\begingroup$ i got the equation $11 (\int_0^x f(x) dx - xf(x)) = 0$ how can i solve this ?? $\endgroup$ – Knight May 13 '14 at 5:32
  • $\begingroup$ Differentiate both sides. and you will get a differential equation. $\endgroup$ – evil999man May 13 '14 at 10:53

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