If f(x)=f(a+x) and $\mathop \smallint \nolimits_0^a \,\,f\left( x \right)\,\,dx = k,\,\,{\rm{then}}\,\,\mathop \smallint \nolimits_0^{na} \,\,f\left( x \right)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

If f(x)=f(a+x) and

\int \nolimits_0^a \,\,f\left( x \right)\,\,dx = k,\,\,\mathrm{then}\,\,\int \nolimits_0^{na} \,\,f\left( x \right)\,\,dx

is equal to

View answer and explanation

Correct option: A

n\,k

Option A (n k) is correct because the integral from 0 to na of f(x) dx is n times the integral from 0 to a of f(x) dx, given that f(x) = f(a+x).

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