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int(-a)^(a)f(x)dx= 2int(0)^(a)f(x)dx, if...

`int_(-a)^(a)f(x)dx= 2int_(0)^(a)f(x)dx,` if f is an even function
0, if f is an odd function.

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To prove the statement regarding the definite integral of the function \( f(x) \) over the interval \([-a, a]\), we will consider two cases: when \( f(x) \) is an even function and when \( f(x) \) is an odd function. ### Step-by-Step Solution **Step 1: Understanding the Definitions** - A function \( f(x) \) is called **even** if \( f(-x) = f(x) \) for all \( x \). - A function \( f(x) \) is called **odd** if \( f(-x) = -f(x) \) for all \( x \). ...
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