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Definite Integration question

2022 · 25 Jul · Shift 2 · Q42

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JEE Main
Mathematics
Definite Integration
2022 · 25 Jul · Shift 2 · Q42

Definite Integration question

2022 · 25 Jul · Shift 2 · Q42

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

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