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JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int\limits_0^x {f\left( t \right)} dt = {x^2} + \int\limits_x^1 {{t^2}f\left( t \right)dt} \), then \(f'(1/2)\) is
- A \(\frac{24}{25}\)
- B \(\frac{18}{25}\)
- C \(\frac{4}{5}\)
- D \(\frac{6}{25}\)
Answer & Solution
Correct Answer
(A) \(\frac{24}{25}\)
Step-by-step Solution
Detailed explanation
Differentiability we get \(f\left( x \right) = 2x - {x^2}f\left( x \right)\) \(f\left( x \right) = \frac{{2x}}{{1 + {x^2}}} \Rightarrow f''\left( x \right) = 2\frac{{\left( {1 - {x^2}} \right)}}{{{{\left( {1 + {x^2}} \right)}^2}}}\)…
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