Given-f-x-f-x-6-x-R-If-2-2-f-x-dx-2-and-2-4-f-x-dx-2-find-the-value-of-4-10-f-x-dx-

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Question Number 131146 by EDWIN88 last updated on 02/Feb/21

$$Givenf\left(x\right)=f(x+6)\mathrm{\forall }x\in \mathbb{R}$$$$If{\int }_{-2}^{2}f\left(x\right)dx=-2and{\int }_{-2}^{4}f\left(x\right)dx=2$$$$findthevalueof{\int }_4^{10}f\left(x\right)dx.$$

Commented by EDWIN88 last updated on 02/Feb/21

$$\Rightarrow {\int }_{-2}^{4}f\left(x\right)dx={\int }_{-2}^{4}f(x+6)dx=2$$$${\int }_4^{10}f\left(x\right)dx=2$$

Answered by Ar Brandon last updated on 02/Feb/21

$$\mathrm{Let}\mathrm{x}-6=\mathrm{u}$$$$\Rightarrow \mathcal{I}={\int }_{-2}^4\mathrm{f}(\mathrm{u}+6)\mathrm{du}={\int }_{-2}^4\mathrm{f}\left(\mathrm{u}\right)\mathrm{du}=2$$

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