Can the following be proven? I do psychology for a living, not math, so I'm relatively clueless.
There are two functions, f(t) and g(t), continuous and differentiable everywhere (etc), such that
int (from t=x to t=x+k) of f(t)dt = int (from t=x to t=x+ak) of g(t)dt
over all x, where k and a are constants. In other words, the definite integrals of the two functions are equal, but g(t) must always be integrated over "a" times the range of f(t).
Can the following be proven?
df/dt = a*(dg/dt)
All responses will be gratefully acknowledged.
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