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Definite Integration question

2025 · 29 Jan · Shift 1 · Q49

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JEE Main
Mathematics
Definite Integration
2025 · 29 Jan · Shift 1 · Q49

Definite Integration question

2025 · 29 Jan · Shift 1 · Q49

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

f:(0, \infty) \rightarrow \mathbf{R}

be a twice differentiable function. If for some

a e 0, \int\limits_0^1 f(\lambda x) \mathrm{d} \mathrm{\lambda}=a f(x), f(1)=1

and

f(16)=\frac{1}{8}

, then

16-f^{\prime}\left(\frac{1}{16}\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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