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

  • question_answer
    \[\int_{0}^{2n\pi }{\left( |\sin x|-\left. \left| \frac{1}{2}\sin x \right. \right| \right)}\ dx\] equals  [Orissa JEE 2005]

    A)                 n            

    B)                 2n

    C)                 ?2n       

    D)                 None of these

    Correct Answer: B

    Solution :

               \[\int_{0}^{2n\pi }{\left( |\sin x|-\frac{1}{2}|\sin x| \right)}\ dx\]=\[\frac{1}{2}\int_{0}^{2n\pi }{\ \ \ \ |\sin x|dx}\]                                 \[=\frac{2n}{2}\times 2\int_{0}^{\pi /2}{\sin x\ dx=2n}[-\cos x]_{0}^{\pi /2}=2n.\]


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