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

  • question_answer
    \[\int_{{}}^{{}}{{{\cos }^{3}}x\ {{e}^{\log (\sin x)}}}\ dx\] is equal to

    A)            \[-\frac{{{\sin }^{4}}x}{4}+c\]

    B)            \[-\frac{{{\cos }^{4}}x}{4}+c\]

    C)            \[\frac{{{e}^{\sin x}}}{4}+c\]

    D)            None of these

    Correct Answer: B

    Solution :

                       \[\int_{{}}^{{}}{{{\cos }^{3}}x\,\,{{e}^{\log \sin x}}dx}=\int_{{}}^{{}}{{{\cos }^{3}}x\sin x\,dx}\]            \[=-\int_{{}}^{{}}{{{t}^{3}}dt}=-\frac{{{t}^{4}}}{4}+c=-\frac{{{\cos }^{4}}x}{4}+c\] \[\{\text{Putting}\,t=\cos x]\].


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