If $f(x)$ is a periodic function, with period $T$, then

$\int_\limits a^b f(x) d x=\int_\limits a^{b+T} f(x) d x$

$\int_\limits a^b f(x) d x=\int_\limits {a+T}^b f(x) d x$

$\int_\limits a^b f(x) d x=\int_\limits{a+T}^{b+2 T} f(x) d x$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Understanding +4 | -1

f(x)

is a periodic function, with period

T

, then

View answer and explanation

Correct option: C

\int\limits_{a}^b f(x) d x=\int\limits_{{a+T}}^{b+T} f(x) d x

Option C is correct because shifting the integration limits by the period T of a periodic function does not change the value of the definite integral.

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