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  • Please solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 28 maths textbook solution.

Please solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 28 maths textbook solution.

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Answer:- 0

Hints:-  You must know the integration rules of trignometry functions.

Given:-  \int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x

Solution : f(x)=\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x

               \begin{aligned} f(-x) &=\log \left(\frac{2+\sin x}{2-\sin x}\right) d x \\ f(-x) &=-\log \left(\frac{2-\sin x}{2+\sin x}\right) d x \\ &=f(-x) \\ &=-f(x) \end{aligned}

\therefore f(x) is an odd function

                \therefore \int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x=0

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