$\int_{0}^{2}\,f(x)dx = 2$
$\therefore F(2)-F(0) = 2$
$\int_{0}^{\frac{\pi }{4} }\,f(2 tan x)sec^2 xdx$
ให้ $u = 2 tan x \Rightarrow \frac{du}{dx} = 2 sec^2 x \Rightarrow dx = \frac{du}{2 sec^2 x}$
$\int_{0}^{\frac{\pi }{4} }\,f(2 tan x)sec^2 xdx = \int_{0}^{2}\,f(u) sec^2 x \frac{du}{sec^2 x} = \frac{1}{2} [F(2)-F(0)] = 1 $
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