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  • Please solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 30 maths textbook solution.

Please solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 30 maths textbook solution.

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Answer:- 0

Hints:-  You must know the integral rules of trignometric functions and odd even functions.

Given:-  \int_{-a}^{a} \log \left(\frac{a-\sin \theta}{a+\sin \theta}\right) d \theta, a>0

Solution : f(x)=\log \left(\frac{a-\sin \theta}{a+\sin \theta}\right)

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

f(x) is an odd function

         \therefore \int_{-a}^{a} \log \left(\frac{a-\sin \theta}{a+\sin \theta}\right) d \theta=0

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