Question:medium
Let f be a twice differentiable non-negative function such that \((f(x))^2 = 25 + \int_0^x ( f(t)^2 + (f'(t))^2 ) dt\). Then the mean of \(f(\log_2(1)), f(\log_2(2)), \dots, f(\log_2(625))\) is equal to :
Let f be a twice differentiable non-negative function such that \((f(x))^2 = 25 + \int_0^x ( f(t)^2 + (f'(t))^2 ) dt\). Then the mean of \(f(\log_2(1)), f(\log_2(2)), \dots, f(\log_2(625))\) is equal to :
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In integral equations, the first step is almost always differentiating both sides using the Leibniz Rule to convert it into a differential equation.
Updated On: Feb 24, 2026
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Correct Answer: 1565
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