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If $$\displaystyle f\left ( 2a-x \right )=f\left (x  \right )$$ and $$\displaystyle \int_{0}^{a}f\left ( x \right )dx=\lambda $$, then $$\displaystyle \int_{0}^{2a}f\left ( x \right )dx$$ is


A
2λ
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B
λ
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C
0
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D
none of these
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Solution

The correct option is A $$\displaystyle 2\lambda $$
We know that:-

$$\displaystyle\int_{0}^{2a}f(x)dx=2\int_{0}^{a}f(x)dx $$  when, $$f(2a-x)=f(x)$$

Hence, $$\displaystyle\int_{0}^{2a}f(x)dx=2\int_{0}^{a}f(x)dx$$

$$=2\lambda$$

Hence, answer is option-(A).

Mathematics

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