Let f be a twice differentiable function on R. If f^{'}(0)=4 and f(x)+\int_{0}^{x}(x-t) f^{'}(t) d t=(e^{2 x}+e^{-2 x}) \cos 2 x+\frac{2}{a} x, then (2 a+1)^{5} a^{2} is equal to ___ [25-Jul-2022-Shift-2]

JEE Mains 25-July-2022 Shift 2 Solved Paper

Section: Mathematics

Question : 26 of 90

Marks: +1, -0

Let f be a twice differentiable function on R. If f′(0)=4 and f(x)+

∫

(x−t)f′(t)dt=(e2x+e−2x)‌cos‌2‌x+‌

x, then (2a+1)5a2 is equal to ___

[25-Jul-2022-Shift-2]

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