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Definite Integration question

2023 · 24 Jan · Shift 2 · Q42

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PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 24 Jan · Shift 2 · Q42

Definite Integration question

2023 · 24 Jan · Shift 2 · Q42

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

f

be

a

differentiable function defined on

\left[ {0,{\pi \over 2}} \right]

such that

f(x) \gt 0

and

f(x) + \int_0^x {f(t)\sqrt {1 - {{({{\log }_e}f(t))}^2}} dt = e,\forall x \in \left[ {0,{\pi \over 2}} \right]}

. Then

\left( {6{{\log }_e}f\left( {{\pi \over 6}} \right)} \right)^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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