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Question Number 212314 by Spillover last updated on 09/Oct/24

Answered by mehdee7396 last updated on 09/Oct/24

$$f\left(x\right)=ln\left(\frac{2-sinx}{2+sinx}\right)$$$$f(-x)=ln\left(\frac{2+sinx}{2-sinx}\right)=-f\left(x\right)$$$$\Rightarrow ;f;is;odd\Rightarrow {\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}f\left(x\right)dx=0✓$$$$$$

Answered by Ghisom last updated on 09/Oct/24

$$f\left(x\right)=\ln \frac{2-\sin x}{2+\sin x}$$$$f(-x)=\ln \frac{2+\sin x}{2-\sin x}=-\ln \frac{2-\sin x}{2+\sin x}=-f\left(x\right)$$$$\Rightarrow \underset{-a}{\stackrel{a}{\int }}f\left(x\right)dx=0$$

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