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MathsJEE Main 4 Apr 2026, Shift 2·Q25·Numerical·Tough

Differential Equations · Integral equation to differential equation

Let ff be a twice differentiable function such that f(x)=∫0xtan⁡(t−x) dt−∫0xf(t)tan⁡t dt,x∈(−π2,π2)f(x) = \int_0^x\tan(t - x)\,dt - \int_0^x f(t)\tan t\,dt,\quad x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) Then f′′(π6)+12f′(−π6)+f(π6)f''\left(\dfrac{\pi}{6}\right) + 12f'\left(-\dfrac{\pi}{6}\right) + f\left(\dfrac{\pi}{6}\right) is equal to .

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