Let f be a twice differentiable function on R. If f^()(0)=4 and f(x) + ∫₀ˣ (x - t)f'(t)dt = (e²ˣ + e⁻²ˣ) cos 2x + 2/ax, then (2 a+1)⁵ a² is equal to _ _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Evening shift · Q32

JEE Main 202225 Jul, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let

f

be a twice differentiable function on

\mathbb{R}

. If

f^{\prime}(0)=4

and

f(x) + \int\limits_0^x {(x - t)f'(t)dt = \left( {{e^{2x}} + {e^{ - 2x}}} \right)\cos 2x + {2 \over a}x}

, then

(2 a+1)^{5}\, a^{2}

is equal to _______________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 Integral Calculus Question with Answer (25 Jul Evening shift, Q32) | JEE Arc