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Let $f (x) = \int_{1}^{x} \sqrt{2 - t^{2}} d t .$ Then the real roots of the equation $x^{2} - f^{'} (x) = 0$ are

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Correct option is A

Using Property 18, we have f′(x)=2−x2and thus the given equation reduces to x2−2−x2=0 ⇒x2+2x2−1=0. Thus the real roots are given by x = ± 1.

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Let f(x)=∫1x 2−t2dt. Then the real roots of the equation x2−f′(x)=0 are

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Let $f (x) = \int_{1}^{x} \sqrt{2 - t^{2}} d t .$ Then the real roots of the equation $x^{2} - f^{'} (x) = 0$ are