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Question Number 77339 by naka3546 last updated on 05/Jan/20

Commented by mr W last updated on 05/Jan/20

$${\int }_3^{6}f\left(x\right)dx=-2$$$$buti{don}^{\prime }tthinkwecanget$$$${\int }_3^{5}f\left(x\right)dx$$$$withgivenconditions.$$

Commented by msup trace by abdo last updated on 05/Jan/20

$$\Rightarrow f\left(x\right)=f(x-3)\Rightarrow$$$${\int }_3^{5}f\left(x\right)dx={\int }_3^{5}f(x-3)dx$$$${=}_{x-3=t}{\int }_0^{2}f\left(t\right)dt$$$$wehavealso{\int }_{-3}^{6}f\left(x\right)dx=-6\Rightarrow$$$${\int }_{-3}^{6}f(x+3)dx=-6(ch.x+3=u)$$$$\Rightarrow {\int }_0^{9}f\left(u\right)du=-6$$$$conditionnotcompatible...$$$$$$

Answered by john santu last updated on 06/Jan/20

$$\underset{-3+3}{\stackrel{6+3}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=-6$$$$\underset{0}{\stackrel{9}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=-6\Rightarrow \underset{3}{\stackrel{12}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=-6$$$$\underset{3}{\stackrel{5}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}+\underset{5}{\stackrel{12}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=-6$$$$\underset{3}{\stackrel{5}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=-6-\underset{5}{\stackrel{12}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$$$$$$

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