∫0α/3f(x)f(x)+fα−3x3 dx=

∫0α/3f(x)f(x)+fα−3x3 dx ∫0α/3 f(x)f(x)+fα3-x =α3-02=α6

∫0α/3f(x)f(x)+fα−3x3 dx=

∫0α/3f(x)f(x)+fα−3x3 dx ∫0α/3 f(x)f(x)+fα3-x =α3-02=α6

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$\int_{0}^{α / 3} \frac{f (x)}{f (x) + f (\frac{α - 3 x}{3})} d x =$

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$\frac{2 α}{3}$

$\frac{α}{2}$

$\frac{α}{3}$

$\frac{α}{6}$

answer is D.

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Detailed Solution

$\begin{array}{rcl} \int_{0}^{α / 3} \frac{f (x)}{f (x) + f (\frac{α - 3 x}{3})} dx \\ \int_{0}^{α / 3} \frac{f (x)}{f (x) + f (\frac{α}{3} - x)} \\ = & \frac{\frac{α}{3} - 0}{2} = \frac{α}{6} \end{array}$

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∫0α/3f(x)f(x)+fα−3x3 dx=

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$\int_{0}^{α / 3} \frac{f (x)}{f (x) + f (\frac{α - 3 x}{3})} d x =$