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

  • question_answer
    \[\int_{\,0}^{\,\pi }{{{\cos }^{3}}x\,dx=}\]            [MP PET 1996; Pb. CET 2002]

    A)                 \[-1\]    

    B)                 0

    C)                 1             

    D)                 \[\pi \]

    Correct Answer: B

    Solution :

               \[\int_{0}^{\pi }{{{\cos }^{3}}xdx=\int_{0}^{2.\frac{\pi }{2}}{{{\cos }^{3}}x\,dx=0}}\],                                                                                 \[\{\because \,\,{{\cos }^{3}}(\pi -x)=-{{\cos }^{3}}x\}\].


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