Mathematics · 2014
JEE Main · 12 April 2014, Shift 1 · Q76
If for a continuous function f(x), ∫_-π^t (f(x)+x) d x=π^2- t^2, for all t ≥-π, then f(-(π)/3) is equal to:
If for a continuous function $\displaystyle f(x)$, $\displaystyle \int_{-\pi}^{\mathrm{t}}(f(x)+x) \mathrm{d} x=\pi^2-\mathrm{t}^2$, for all $\displaystyle \mathrm{t} \geqslant-\pi$, then $\displaystyle f\left(-\frac{\pi}{3}\right)$ is equal to :
Official answer
(1)
$\displaystyle \pi$
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JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.