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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1
If ∫ab{f(x)−3x}dx=a2−b2\int_a^b\{f(x)-3 x\} d x=a^2-b^2, then the value of f(π6)f\left(\frac{\pi}{6}\right), is
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Correct option: A
π6\frac{\pi}{6}
The correct answer is A (π6\frac{\pi}{6}) because after evaluating the integral and differentiating, we find that f(x)=xf(x) = x, thus f(π6)=π6f(\frac{\pi}{6}) = \frac{\pi}{6}.

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