Let f: R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x R where k > 0 and n is a positive integer. If I₁ = ∫₀^(4nk) f(x)dx and I₂ = ∫ - k ^(3k) f(x)dx, then:

Integral Calculus: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jun, Evening shift · Q3429

JEE Main 202228 Jun, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let f : R

\to

R be a continuous function satisfying f(x) + f(x + k) = n, for all x

\in

R where k > 0 and n is a positive integer. If

{I_1} = \int\limits_0^{4nk} {f(x)dx}

and

{I_2} = \int\limits_{ - k}^{3k} {f(x)dx}

, then :