Let f be a twice differentiable function such that f(x)=∫₀ˣ tan (t-x) dt-∫₀ˣ f(t) tan t dt, x (- π2, π2). Then f''(π6)+12f'(- π6)+f(π6) is equal to _ _ _

Integral Calculus: JEE Main 2026 Mathematics question

JEE Main 2026 · 4 Apr, Evening shift · Q25

JEE Main 20264 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let

f

be a twice differentiable function such that

f(x)=\int_0^x\tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt

x\in\left(-\frac\pi2,\frac\pi2\right)

. Then

f''\left(\frac\pi6\right)+12f'\left(-\frac\pi6\right)+f\left(\frac\pi6\right)

is equal to ______

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2026 Integral Calculus Question with Solution (4 Apr Evening shift, Q25) | JEE Arc