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Question Number 192289 by cortano12 last updated on 14/May/23

$$\underset{-\mathrm{e}}{\stackrel{\mathrm{e}}{\int }}\frac{\sin \mathrm{x}}{\sec {}^2\mathrm{x}+1}\mathrm{dx}=?$$

Answered by mehdee42 last updated on 14/May/23

$$f\left(x\right)=\frac{sinx}{{secx}^{2}x+1}\Rightarrow f(-x)=f\left(x\right)$$$$\Rightarrow {\int }_{-e}^e\frac{sinx}{{sec}^{2}x+1}dx=0$$

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