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Definite Integration question

2022 · 28 Jun · Shift 2 · Q29

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 28 Jun · Shift 2 · Q29

Definite Integration question

2022 · 28 Jun · Shift 2 · Q29

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

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 :

A
${I_1} + 2{I_2} = 4nk$
B
${I_1} + 2{I_2} = 2nk$
C
${I_1} + n{I_2} = 4{n^2}k$
D
${I_1} + n{I_2} = 6{n^2}k$

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