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Question Number 127616 by bramlexs22 last updated on 31/Dec/20

$$\mathrm{If}{\int }_1^4\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=6,\mathrm{then}{\int }_1^4\mathrm{f}(5-\mathrm{x})\mathrm{dx}?$$

Commented by liberty last updated on 31/Dec/20

$$\mathrm{let}5-\mathrm{x}=\mathrm{X}\Rightarrow \mathrm{dx}=-\mathrm{dX}$$$$\mathrm{if}\mathrm{x}=4\Rightarrow \mathrm{X}=1\wedge \mathrm{if}\mathrm{x}=1\Rightarrow \mathrm{X}=4$$$$\mathrm{then}{\int }_1^4\mathrm{f}(5-\mathrm{x})\mathrm{dx}={\int }_4^1\mathrm{f}\left(\mathrm{X}\right)(-\mathrm{dX})$$$$={\int }_1^4\mathrm{f}\left(\mathrm{X}\right)\mathrm{dX}=6.$$$$\mathrm{hahaha}$$

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