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JEE Main & Advanced Mathematics Definite Integration Question Bank Fundamental definite integration, Definite integration by substitution

  • question_answer
    The greater of \[\int_{0}^{\pi /2}{\frac{\sin x}{x}\,dx}\] and \[\frac{\pi }{2},\] is

    A)                 \[\frac{\pi }{2}\]              

    B)                 \[\int_{0}^{\pi /2}{\frac{\sin x}{x}\,dx}\]

    C)                 Nothing can be said       

    D)                 None of these

    Correct Answer: A

    Solution :

               Since \[\sin x<x\] for \[0<x\le \pi /2\]                                 So, \[\int_{0}^{^{\pi /2}}{\frac{\sin x}{x}dx<\int_{0}^{\pi /2}{1dx=\frac{\pi }{2}}}\].


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