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Question:
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$$
\int_{-a}^a f(x) d x-\int_0^a f(-x) d x=
$$
Options:
\int_{-a}^a f(x) d x-\int_0^a f(-x) d x=
$$
Solution:
1090 Upvotes
Verified Answer
The correct answer is:
$\int f(a \quad x) d x$
$$
\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}
$$
by using $(\mathrm{a}+0-\mathrm{x})$ property
$\Rightarrow \int_0^a \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{dx}$
\begin{aligned}
& \text { } \int_{-a}^a f(x) d x-\int_0^a f(-x) d x \\
& \because \int_{-a}^a f(x) d x=\int_0^a f(x) d x+\int_0^a f(-x) d x \\
& \Rightarrow \int_0^a f(x) d x
\end{aligned}
$$
by using $(\mathrm{a}+0-\mathrm{x})$ property
$\Rightarrow \int_0^a \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{dx}$
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