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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration of Rational Function by Using Partial Fractions

  • question_answer
    If \[\int_{{}}^{{}}{\sin 5x\cos 3x\ dx=-\frac{\cos 8x}{16}}+A\], then \[A=\]            [MP PET 1992]

    A)                 \[\frac{\sin 2x}{16}+\]constant

    B)                 \[-\frac{\cos 2x}{4}+\]constant

    C)                 Constant

    D)                 None of these

    Correct Answer: B

    Solution :

                       \[\int_{{}}^{{}}{\sin 5x\cos 3x\ dx}=\frac{1}{2}\int_{{}}^{{}}{(\sin 8x+\sin 2x)}dx\]                                                   \[=\frac{-\cos 8x}{16}-\frac{\cos 2x}{4}+c\]                 Equating to the given value, we get \[A=\frac{-\cos 2x}{4}+c\].


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