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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration by Parts

  • question_answer
    If \[\frac{d}{dx}f(x)=x\cos x+\sin x\] and \[f(0)=2\], then \[f(x)=\] [MP PET 1989]

    A)                 \[x\sin x\]

    B)                 \[x\cos x+\sin x+2\]

    C)                 \[x\sin x+2\]

    D)                 \[x\cos x+2\]

    Correct Answer: C

    Solution :

                    \[\frac{d}{dx}f(x)=x\cos x+\sin x\]                 \[\Rightarrow f(x)=\int_{{}}^{{}}{(x\cos x+\sin x)\ dx}=x\sin x+c\]                 Since, \[f(0)=2\Rightarrow c=2\];  \[\therefore \ f(x)=x\sin x+2\].


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