Find $int_0^1f(x)dx$ ?

Question

$f:RR->RR$ , continuous in $RR$ with $f(x)e^x+f(e^(-x))=xe^x+e^(-x)$
, $AA$ $x$ $in$ $RR$

Find $int_0^1f(x)dx$

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Answer 1 · 2018-05-30T12:28:27

Shown below:

By inspection, $f(x) = x$

$=> int_0 ^1 x dx$

$int x^n dx = 1/(n+1) x^(n+1) + c$

$=> int_0 ^1 x^1 dx = [1/2 x^2 ]_0 ^1$

$=> ( 1/2 * 1^2 ) - ( 1/2 * 0^2 )$

$= 1/2$