NVAMediumJEE Main 2026 · 23 January, Shift 1Linear Differential Equations

Mathematics Question from JEE Main 2026 · 23 January, Shift 1

Let ff be a twice differentiable non-negative function such that (f(x))2=25+∫0x(f(t)2+(f′(t))2) dt(f(x))^2 = 25 + \int_0^x ( f(t)^2 + (f'(t))^2 ) \, dt. Then the mean of f(log⁡e(1)),f(log⁡e(2)),…,f(log⁡e(625))f(\log_e(1)), f(\log_e(2)), \dots, f(\log_e(625)) is equal to :

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