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  • Please solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 45 Subquestion (ii) maths textbook solution.

Please solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 45 Subquestion (ii) maths textbook solution.

Answers (1)

Answer:-  Proved

Hints:-  You must know the rules of integration.

Given:-  f is an integrable function

Solution:- We have, f is an integrable function

                I=\int_{-a}^{a} x f\left(x^{2}\right) d x

Let

            \begin{aligned} &f(x)=x f\left(x^{2}\right) \\ &f(-x)=-x f\left(x^{2}\right) \\ &=-f(x) \end{aligned}

Hence it is an odd function

Using integration property,

If function is odd, \int_{-a}^{a} f(x) d x=0

           \therefore \int_{-a}^{a} x \cdot f\left(x^{2}\right) d x=0

Hence proved

Posted by

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