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Question Number 125511 by sandy_delta last updated on 11/Dec/20

$$\mathrm{if}:$$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}(-\mathrm{x})\mathrm{for}\mathrm{x}\in \mathbb{R}$$$$\underset{-3}{\stackrel{3}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=0$$$$\underset{-2}{\stackrel{3}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=5$$$$\mathrm{then}\underset{0}{\stackrel{2}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=?$$

Commented by liberty last updated on 11/Dec/20

$$\Rightarrow \underset{-3}{\stackrel{3}{\int }}f\left(x\right)dx=2\underset{0}{\stackrel{3}{\int }}f\left(x\right)dx=0;\underset{0}{\stackrel{3}{\int }}f\left(x\right)dx=0$$$$\underset{-2}{\stackrel{3}{\int }}f\left(x\right)dx=\underset{-2}{\stackrel{0}{\int }}f\left(x\right)dx+\underset{0}{\stackrel{3}{\int }}f\left(x\right)dx$$$$5=\underset{0}{\stackrel{2}{\int }}f\left(x\right)dx+0$$$$5=\underset{0}{\stackrel{2}{\int }}f\left(x\right)dx$$

Commented by sandy_delta last updated on 12/Dec/20

$$\mathrm{thank}\mathrm{you}$$

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