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e-e-sin-x-sec-2-x-1-dx-




Question Number 192289 by cortano12 last updated on 14/May/23
        ∫_(−e) ^e  ((sin x)/(sec^2 x+1)) dx =?
$$\:\:\:\:\:\:\:\:\underset{−\mathrm{e}} {\overset{\mathrm{e}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\:\mathrm{dx}\:=? \\ $$
Answered by mehdee42 last updated on 14/May/23
f(x)=((sinx)/(secx^2 x+1))⇒f(−x)=f(x)  ⇒∫_(−e) ^e   ((sinx)/(sec^2 x+1)) dx=0
$${f}\left({x}\right)=\frac{{sinx}}{{secx}^{\mathrm{2}} {x}+\mathrm{1}}\Rightarrow{f}\left(−{x}\right)={f}\left({x}\right) \\ $$$$\Rightarrow\int_{−{e}} ^{{e}} \:\:\frac{{sinx}}{{sec}^{\mathrm{2}} {x}+\mathrm{1}}\:{dx}=\mathrm{0} \\ $$

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