$$ \int_{-a}^a f(x) d x-\int_0^a f(-x) d x= $$

$$ \int_{-a}^a f(x) d x-\int_0^a f(-x) d x= $$
  1. $\int_{-a}^a f(a-x) d x$
  2. $\int_{-a}^a f(x)+f(a-x) d x$
  3. $\int_0^a f(x)+f(a-x) d x$
  4. $\int f(a \quad x) d x$

Solution

$ \begin{aligned} & \text { } \int_{-a}^a f(x) d x-\int_0^a f(-x) d x \\ & \because \int_{-a}^a f(x) d x=\int_0^a f(x) d x+\int_0^a f(-x) d x \\ & \Rightarrow \int_0^a f(x) d x \end{aligned} $ by using $(\mathrm{a}+0-\mathrm{x})$ property $\Rightarrow \int_0^a \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{dx}$

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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