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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration by Substitution

  • question_answer
    \[\int_{{}}^{{}}{\frac{1}{\sqrt{x}}}\sin \sqrt{x}\ dx=\]       [MP PET 1989]

    A)            \[-\frac{1}{2}\cos \sqrt{x}+c\]

    B)            \[-2\cos \sqrt{x}+c\]

    C)            \[\frac{1}{2}\cos \sqrt{x}+c\]

    D)            \[2\cos \sqrt{x}+c\]

    Correct Answer: B

    Solution :

                       Put \[\sqrt{x}=t\Rightarrow \frac{1}{\sqrt{x}}\,dx=2dt,\] then it reduces to            \[2\int_{{}}^{{}}{\sin t\,dt}=-2\cos t+c=-2\cos \sqrt{x}+c.\]


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