JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

If for a continuous function

f(x), \int\limits_{{-\pi}}^t(f(x)+x) d x=\pi^2-

t^2

, for all

t \geq-\pi

, then

f\left(-\frac{\pi}{3}\right)

is equal to:

View answer and explanation

Correct option: A

\pi

Option A (

\pi

) is correct because after differentiating the given integral equation and solving for f(x), we find f(-

\frac{\pi}{3}

) =

\pi

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