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hartnn
 one year ago
Best ResponseYou've already chosen the best response.1any more info about f(x) even function or odd function ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1basically you need to use this : \(\huge \int \limits _a^b f(x)dx=\int \limits_a^b f(a+bx)dx\)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\huge I= \int _0^a \frac{f(x)}{f(xa)+f(x)} \\\huge I =\int _0^a \frac{f(ax)}{f(x)+f(ax)} \)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1if f(x)=f(x) then you get your result after adding the above 2 equations....

Jonask
 one year ago
Best ResponseYou've already chosen the best response.0i tried a u=xa substitution

Jonask
 one year ago
Best ResponseYou've already chosen the best response.0no info about even or odd

Jonask
 one year ago
Best ResponseYou've already chosen the best response.0oh sry its ax the original quest\[\huge \int_0^a\frac{f(x)}{f(x)+f(ax)}dx\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1then using that property will directly give you answer.... and ofcourse you have to add 2 equations u got....

Jonask
 one year ago
Best ResponseYou've already chosen the best response.0using\[\frac{ a}{a+b}=\frac{ b }{ a+b }+1\] so \[\int\limits_0^a \frac{ f(x) }{ f(x)+f(ax) }=\int\limits_0^a \frac{ f(ax) }{ f(x)+f(xa)}+1\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1is that required to be used ? you can use the property...

Jonask
 one year ago
Best ResponseYou've already chosen the best response.0u=ax du=dx \[I=()\int_a^0\color{red}{\frac{f(u)}{f(u)+f(au)}}du+\int_0^a1\] red same as I so \[I_0^a+I_a^0=a\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\huge \int \limits _a^b f(x)dx=\int \limits_a^b f(a+bx)dx\)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1you want proof ? i need to look up...

Jonask
 one year ago
Best ResponseYou've already chosen the best response.0no wait before proof let me see what it gives

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.1I remember the proof.

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.1in RHS, let a+bx = t => dx = dt limits also change to x=b to a just substitute and you'll get the LHS
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