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

  • question_answer
    If \[\int{f(x)\cos \,\,x\,\,dx=\frac{1}{2}{{f}^{2}}(x)+c,}\] then \[f(x)\] can be

    A) x

    B) 1

    C) \[\cos x\]

    D) \[sinx\]

    Correct Answer: D

    Solution :

    [d] Since \[\int{f{{[x]}^{n}}f'(x)dx=\frac{{{[f(x)]}^{n+1}}}{n+1}+c}\] \[\therefore \int{f(x)\cos \,\,x\,\,dx=\frac{{{f}^{2}}(x)}{2}+c}\] \[\Rightarrow f'(x)=\cos \,\,x\Rightarrow f(x)=\sin \,\,x\]


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