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artofspeed
 2 years ago
integral: are these two expressions equal?
artofspeed
 2 years ago
integral: are these two expressions equal?

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artofspeed
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{a}f(ax)dx = \int\limits_{}^{}f(0)dx\int\limits_{}^{}f(a)dx = \int\limits_{a}^{0}f(x)dx\]

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

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0It will more easy if you take \(f(x)=1\).

artofspeed
 2 years ago
Best ResponseYou've already chosen the best response.0so it this whole expression correct?

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.0only the first and last expressions can be equated.

artofspeed
 2 years ago
Best ResponseYou've already chosen the best response.0actually, the first and last aren't equal. But what's wrong in the expression?

klimenkov
 2 years ago
Best 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.
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