JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f:R \to R

be a continuous function satisfying

f\left( x \right) + f\left( {x + k} \right) = n,

for all

x \in R

where

k > 0

and

n

is a positive integer. If

{l_1} = \int\limits_0^{4nk} {f\left( x \right)} dx

and

{l_2} = \int\limits_{ - k}^{3k} {f\left( x \right)} dx,

then

View answer and explanation

Correct option: C

{l_1} + n{l_2} = 4{n^2}k

Option D (

{l_1} + n{l_2} = 4{n^2}k

) is correct because it is derived from the periodicity of the function and the properties of definite integrals.

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