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[SOLVED] Find the function f

dwsmith

Well-known member
Feb 1, 2012
1,673
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
Jan 30, 2012
2,492
There are infinitely many such functions. The only thing that you know for sure is that $\int_0^xf(x)\,dx=x_1y_1/4$.