If $a$ is fixed real number such that $f\left( {a - x} \right)\,\, + \,\,f\left( {a + x} \right) = 0$, then $\mathop \smallint \limits_0^{2a} \,\,f\left( x \right)\,\,dx = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

a

is fixed real number such that

f\left( {a - x} \right)\,\, + \,\,f\left( {a + x} \right) = 0

, then

\int \limits_0^{2a} \,\,f\left( x \right)\,\,dx =

View answer and explanation

Correct option: B

\mathrm{0}

Option B (0) is correct because the integral of the function over the interval [0, 2a] is zero due to the property

f(a-x) + f(a+x) = 0

, which implies

f(2a-x) = -f(x)

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