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Please solve RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 38 maths textbook solution

Answers (1)

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Answer:

\int_{a}^{2 a} f(x) d x=\int_{0}^{a} f(x) d x+\int_{0}^{2 a}f(2 a-x) d x

Hint:

Given:

\int_{a}^{2 a} f(x) d x

Solution:

\int_{a}^{2 a} f(x) d x

\begin{aligned} &f(2 a-x)=f(x) \\\\ &\int_{0}^{a} 2 f(x) d x \end{aligned}

\begin{aligned} &=2 \int_{0}^{a} f(x) d x \\\\ &\int_{a}^{2 a} f(x) d x=\int_{0}^{a} f(x) d x+\int_{0}^{2 a}f(2 a-x) d x \end{aligned}

 

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