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12th Class Mathematics Definite Integrals Question Bank Critical Thinking

  • question_answer
    \[\int_{\,\pi }^{\,10\pi }{\,|\sin x|dx}\] is [AIEEE 2002]

    A) 20  

    B) 8

    C) 10  

    D) 18

    Correct Answer: D

    Solution :

    • \[\int_{\pi }^{10\pi }{|\sin x|dx=\int_{0}^{\pi }{|\sin x|dx+\int_{\pi }^{10\pi }{\,\,|\sin x|dx}}}-\int_{0}^{\pi }{\,|\sin x|dx}\]                   
    • \[=\int_{0}^{10\pi }{|\sin x|dx-\int_{0}^{\pi }{\,|\sin x|dx}}\]                   
    • \[=10\int_{\,0}^{\,\pi }{|\sin x|dx-\int_{\,0}^{\,\pi }{\,|\sin x|dx}}\]\[=9\int_{\,0}^{\,\pi }{\sin x\,dx}\]           
    • \[[\because \,|\sin x|\] is periodic with period \[\pi \] and in \[[0,\pi ],\sin x\ge 0]\]           
    • \[=9\,[-\cos x]_{0}^{\pi }=9\,(-\cos \pi +\cos 0)\]\[=9\,(1+1)=18\].


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