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JEE Main & Advanced Mathematics Definite Integration Question Bank Properties of Definite Integration

  • question_answer
    \[\int_{0}^{\pi /2}{{}}(\sin x-\cos x)\log (\sin x+\cos x)\,dx=\]    [SCRA 1986]

    A)                 \[-1\]    

    B)                 1

    C)                 0             

    D)                 None of these

    Correct Answer: C

    Solution :

               Put \[\sin x+\cos x=t\Rightarrow -(\sin x-\cos x)dx=dt\]            Also as \[x=0\]to \[\frac{\pi }{2},t=1\]to 1.                                 Since here limit is ?1 to 1?, therefore the value of integral will be zero,  \[\left\{ \because \int_{a}^{a}{f(x)dx=0} \right\}\].


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