Let f: R → R be continuous...... | JEE Main 2022 | Definite

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JEE MAIN 2022

28-06-22 S2

Question

Let $f: R \rightarrow R$ be continuous function satisfying $f(x)+f(x+k)=n$, for all $x \in R$ where $k>0$ and $n$ is a positive integer. If $I_1=\int_0^{4 n k} f(x) d x$ and $I_2=\int_{-k}^{3 k} f(x) d x$, then

Select the correct option:

A

$\mathrm{l}_1+2 \mathrm{l}_2=4 \mathrm{nk}$

B

$l_1+2 l_2=2 n k$

C

$\mathrm{l}_1+\mathrm{n} \mathrm{l}_2=4 \mathrm{n}^2 \mathrm{k}$

D

$l_1+n l_2=6 n^2 k$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

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