# [SOLVED]Find the function f

#### dwsmith

##### Well-known member
I want to find a function f where the area under the curve is A and the area above it is 3A and $$f(x_1) = y_1$$.
$\int_0^{x_1}fdx = A$
and
$\int_0^{x_1}(y_1 - f)dx = 3A$
What I tried was taking
\begin{align}
\int_0^{x_1}(y_1 - f)dx &= 3\int_0^{x_1}fdx\\
\int_0^{x_1}(y_1 - 4f)dx &= 0
\end{align}
but this doesn't seem to go anywhere.

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
There are infinitely many such functions. The only thing that you know for sure is that $\int_0^xf(x)\,dx=x_1y_1/4$.