JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f: R \in R

be a continuous function given by

f(x+y)=f(x)+f(y)

for all

x, y \in R

.
If

\int_0^2 f(x) d x=\alpha

, then

\int_{-2}^2 f(x) d x

is equal to

View answer and explanation

Correct option: C

The correct answer is C (0) because the given functional equation implies that f(x) is of the form

\lambda x

, making it an odd function, and the integral of an odd function over a symmetric interval is zero.

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