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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 12

  • question_answer
    If \[\int{\sqrt{2}\,\sqrt{1+\sin x}}\,dx=-4\,\cos \,(ax+b)+c,\], then the value of (a, b) is

    A) \[\frac{1}{2},\frac{\pi }{4}\]             

    B) \[1,\frac{\pi }{2}\]

    C) \[1,1\]                          

    D) None of these

    Correct Answer: A

    Solution :

    \[I=\int{\sqrt{2}\,\sqrt{1+\sin x}\,\,dx=\sqrt{2}\int{\left( \sin \frac{x}{2}+\cos \frac{x}{2} \right)\,dx}}\]\[=2\int{\sin \left( \frac{\pi }{4}+\frac{x}{2} \right)}\,\,dx=-4\cos \,\,\left( \frac{x}{2}+\frac{\pi }{4} \right)+c\] On comparing, \[a=\frac{1}{2},\,b=\frac{\pi }{4}.\]


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