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

  • question_answer
    \[\int_{-a}^{a}{\sin x\,f(\cos x)\,dx=}\]                                 [RPET 1997]

    A)                 \[2\int_{0}^{a}{\sin x\,f(\cos x)\,dx}\]  

    B)                 0

    C)                 1             

    D)                 None of these

    Correct Answer: B

    Solution :

               \[I=\int_{-a}^{a}{\sin xf(\cos x)\,dx}\]                    \[f(x)=\sin x\,f(\cos x)\Rightarrow f(-x)=-\sin x\,f(\cos x)\]                    \[\because \,\,\,\,f(x)\]is an odd function                                 \[\therefore \,\,\,I=\int_{{}}^{{}}{f(x)dx=0}\].


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