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Let f(x) be an even function then \(\rm \int_{-a}^{a}f(x)dx=?\)
5. None of these

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Correct Answer - Option 4 : \(2\int_{0}^{a}f(x)dx\)

Concept:

A function is said to even if  f(-x) = f(x)

A function is said to be odd if  f(-x) = -f(x)

Calculation:

For an even function

\(\rm \Rightarrow \int_{-a}^{a}f(x)dx=2\int_{0}^{a}f(x)dx\)

If function is odd then 

\(\rm \Rightarrow \int_{-a}^{a}f(x)dx=0\)

Hence , 4 is correct

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