JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q76

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MathematicsSingle correct+4 / -1Question 76 of 90

If for a continuous function $f(x)$ , $\displaystyle\int_{-\pi}^t(f(x)+x)\,dx=\pi^2-t^2$ , for all $t\ge-\pi$ , then $f\left(-\dfrac\pi3\right)$ is equal to :

\pi

\dfrac\pi2

\dfrac\pi3

\dfrac\pi6

Answer and worked solution

Official answer: A

Differentiate in $t$ : $f(t)+t=-2t$ , so $f(t)=-3t$ and $f\left(-\frac\pi3\right)=\pi$ .

Topics:Fundamental theorem of calculus

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JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 76