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Question Number 49903 by rahul 19 last updated on 12/Dec/18

Commented by rahul 19 last updated on 12/Dec/18

$$Periodoff\left(x\right)=4.$$

Answered by mr W last updated on 12/Dec/18

$$t=2-x\Rightarrow x=2-t\Rightarrow 2+x=4-t$$$$\Rightarrow f\left(t\right)=f(4-t)$$$$t=4-x\Rightarrow x=4-t\Rightarrow 4+x=8-t$$$$\Rightarrow f\left(t\right)=f(8-t)=f(4-t)$$$$\Rightarrow f(x+4)=f\left(x\right)\Rightarrow period=4$$$$f(2+x)=f(2-x)$$$$\Rightarrow {\int }_2^{4}f\left(x\right)dx={\int }_0^{2}f\left(x\right)dx=5$$$${\int }_0^{4}f\left(x\right)dx=10$$$${\int }_{10}^{50}f\left(x\right)dx=10{\int }_0^{4}f\left(x\right)dx=100$$

Commented by mr W last updated on 12/Dec/18

You are welcome!

Commented by rahul 19 last updated on 12/Dec/18

Danke Mien Herr! ��

Commented by mr W last updated on 12/Dec/18

Do you learn German in the school?

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