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MathsJEE Main 23 Jan 2026, Shift 1·Q23·Numerical·Moderate

Differential Equations · Integral equation to differential equation

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\left((f(t))^2 + (f'(t))^2\right)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)), \ldots, f(\log_e(625)) is equal to .

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