play with functions5

Calculus Level 4

Let \(f\):\(R^{+}\rightarrow R\) Be a differential function with \(f(1)\) = 3 and satisfying

\(\int _{ 1 }^{ xy }{ f\left( t \right) } dt\quad =\quad y\int _{ 1 }^{ x }{ f\left( t \right) } dt\quad +\quad x\int _{ 1 }^{ y }{ f\left( t \right) } dt\quad\)

then find\(\quad f\left( e \right)\)

Also try playwithfunctions2

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