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

  • question_answer
    If \[I=\int_{0}^{\pi /4}{\,{{\sin }^{2}}x\,dx}\]and\[J=\int_{0}^{\pi /4}{{{\cos }^{2}}x\,dx,}\] then \[I=\]  [SCRA 1989]

    A)                 \[\frac{\pi }{4}-J\]           

    B)                 \[2J\]

    C)                 \[J\]      

    D)                 \[\frac{J}{2}\]

    Correct Answer: A

    Solution :

                    Adding \[I+J=\int_{0}^{\pi /4}{dx=\frac{\pi }{4}\Rightarrow I=\frac{\pi }{4}-J}\].


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