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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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If ∫  x f(x)  dx=  f(x)2\int \,\,x\,\mathrm{ }f\left( x \right)\,\,dx = \,\,\frac{{f\left( x \right)}}{2}, then f(x)f\left( x \right) is equal to
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Correct option: D
ex22\frac{{{e^{{x^2}}}}}{2}
Option D (ex22\frac{{{e^{{x^2}}}}}{2}) is correct because when substituted into the integral equation, it satisfies the given condition.

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