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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Self Evaluation Test - Integrals

  • question_answer
    Let \[f:(0,\infty )\to R\] and \[F(x)=\int\limits_{0}^{x}{f(t)dt}\].If \[F({{x}^{2}})={{x}^{2}}(1+x),\] then \[f(4)\] equals

    A) \[\frac{5}{4}\]

    B) 7

    C) 4

    D) 2

    Correct Answer: C

    Solution :

    [c] \[F'(x)=f(x)\] Also, \[F(t)=t\left( 1+\sqrt{t} \right)\] \[\Rightarrow F'(t)=1+\frac{3}{2}{{t}^{1/2}};F'(4)=1+3=4\Rightarrow f(4)=4\]


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