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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1
Let f(x)=∫1x  2  −  t2 dtf\left( x \right) = \int \nolimits_1^x \,\,\sqrt {2\,\, - \,\,{t^2}} \,dt.〗 Then, real roots of the equation x2−f′(x)=0{x^2} - f'\left( x \right) = 0 are
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Correct option: A
±  1\pm \,\,1
Option A (±  1\pm \,\,1) is correct because these are the real roots obtained by solving the equation x2−f′(x)=0{x^2} - f'\left( x \right) = 0 after finding f′(x)f'(x).

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