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Explain solution for  RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 25 Subquestion (ii) maths textbook solution.

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Hints:-  You must know the integral rules of logarithmic functions.

Given:-  \int_{-\pi}^{\pi}\left(1-x^{2}\right) \sin x \cdot \cos ^{2} x \cdot d x

Solution : \int_{-\pi}^{\pi}\left(1-x^{2}\right) \sin x \cdot \cos ^{2} x \cdot d x=f(x)

                \begin{aligned} &f(-x)=-\left(1-x^{2}\right) \sin x \cdot \cos ^{2} x\\ &=-f(x) \text {, is an odd function }\\ &I=\int_{-\pi}^{\pi}\left(1-x^{2}\right) \sin x \cdot \cos ^{2} x . d x=0 \end{aligned}

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