For some function $f(x)$ and $g(x)$ which is differentiable in all positive real numbers, following conditions (A), (B), and (C) are true.

(A) $(\frac{f(x)}{x})'$ = $x^2 e^{-x^2}$

(B) $g(x) =\frac{4}{e^4} \int_{1}^{x} e^{t^2} f(t) dt$

(C) $f(1) = \frac{1}{e}$

calculate the value of $f(2) - g(2)$

8/e^4
6/e^4
16/3e^4
22/3e^4
20/3e^4

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Although solution is written in Korean, I suppose any math-lover would have no problem understanding this.