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Odd and even function:
If a function f(x) such that f(-x) = f(x) then f(x) is an even function and if f(-x) = -f(x) then f(x) is an odd function.
Integration of odd and even function:
The following two cases hold for a differentiable function f(x).
If f(x) is an even function then
If f(x) is an odd function then
Calculation:
Let
Therefore, f(-x) = f(x) implies that f(x) is an even function.
Thus, the integral is given by,
Hence, the value of the given integral is 2.
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