# Find f with A plane curve whose equation is $y - f (x) = 0$ passes through the origin.

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.

## 1 Answer

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

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

Can you do it now?

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