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JEE Main & Advanced Sample Paper JEE Main Sample Paper-31

  • question_answer
    The value of definite integral \[\int\limits_{0}^{\frac{\pi }{2}}{\sin \left( {{\sin }^{-1}}[x] \right)dx}\] is equal to [Note: \[[k]\] denote the largest integer less than or equal to k]

    A) \[\pi -1\]

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

    C) \[\frac{\pi -2}{2}\]

    D) \[\frac{\pi }{4}\]

    Correct Answer: C

    Solution :

    Let \[f(x)=\sin ({{\sin }^{-1}}[x])=\left\{ \begin{matrix}    0, & 0\le x<1  \\    1, & 1\le x<\frac{\pi }{2}  \\ \end{matrix} \right.\] \[\therefore I=\int\limits_{0}^{1}{0}dx+\int\limits_{1}^{\frac{\pi }{2}}{1dx=0}+\left( \frac{\pi }{2}+1 \right)=\frac{\pi -2}{2}\]


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