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Question Number 131807 by Fikret last updated on 08/Feb/21

$$f\left(x\right)=2-x\underset{0}{\stackrel{1}{\int }}f\left(x\right)dx\Rightarrow \underset{0}{\stackrel{1}{\int }}f\left(x\right)dx=?$$$$$$$$$$

Commented by Fikret last updated on 08/Feb/21

$$f\left(x\right)=2-x.\underset{0}{\stackrel{1}{\int }}f\left(x\right)dx\Rightarrow \underset{0}{\stackrel{1}{\int }}f\left(x\right)dx=?$$$$$$$$$$

Answered by mr W last updated on 08/Feb/21

$$say{\int }_0^{1}f\left(x\right)dx=c$$$$f\left(x\right)=2-cx$$$${\int }_0^{1}f\left(x\right)dx={[2x-\frac{{cx}^2}{2}]}_0^1=2-\frac{c}{2}=c$$$$\Rightarrow c=\frac{4}{3}={\int }_0^{1}f\left(x\right)dx$$

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