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JEE Advanced Mathematics question

MathematicsDefinite IntegrationJEE Advanced

Let be a differentiable function such that . If for all then the value of is

Answer: 6

Solution

Differentiate both sides w.r.t. (Leibniz rule):

6f(x) = 3f(x) + 3xf'(x) - ⇒ xf'(x) - f(x) = ⇒ - Missing argument for \frac\frac1x y = x (y = f(x)).

Integrating factor e^{-\int\frac{dx}{x}}e^{-\ln x}$

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Question ID VK-110810