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

  • question_answer
    If \[\int_{{}}^{{}}{x\sin xdx=-x\cos x+A}\], then \[A=\] [MP PET 1992, 2000; RPET 1997]

    A)                 \[\sin x+\]Constant

    B)                 \[\cos x+\]Constant

    C)                 Constant

    D)                 None of these

    Correct Answer: A

    Solution :

                    Since,\[\int_{{}}^{{}}{x\sin x\,dx}=-x\cos x+A\]                 \[\Rightarrow -x\cos x+\sin x+\text{constant}=-x\cos x+A\]                 Equating it, we get \[A=\sin x+\text{constant}\text{.}\]


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