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artofspeedBest ResponseYou've already chosen the best response.0
\[\int\limits_{0}^{a}f(ax)dx = \int\limits_{}^{}f(0)dx\int\limits_{}^{}f(a)dx = \int\limits_{a}^{0}f(x)dx\]
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
You can check this on example. Try \(f(x)=x^2, a=1.\)
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
It will more easy if you take \(f(x)=1\).
 one year ago

artofspeedBest ResponseYou've already chosen the best response.0
so it this whole expression correct?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.0
only the first and last expressions can be equated.
 one year ago

artofspeedBest ResponseYou've already chosen the best response.0
actually, the first and last aren't equal. But what's wrong in the expression?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
\[\int\limits_{0}^{a}f(ax)dx \ne \int\limits_{}^{}f(0)dx\int\limits_{}^{}f(a)dx = \int\limits_{a}^{0}f(x)dx\]The primitive of \(f(ax)\) is \(\int f(ax)dx\) and not \(\int f(ax)dx\). You can check this by taking derivative. Now, I think you can answer your question by yourself.
 one year ago
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