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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{{{\sin }^{-1}}}(\cos x)dx=\]

    A)            \[\frac{\pi x}{2}\]

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

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

    D)            \[\frac{\pi x+{{x}^{2}}}{2}\]

    Correct Answer: C

    Solution :

               \[\int_{{}}^{{}}{{{\sin }^{-1}}(\cos x)\,dx}=\int_{{}}^{{}}{\left\{ \frac{\pi }{2}-{{\cos }^{-1}}(\cos x) \right\}}\,dx\]                    \[=\frac{\pi }{2}x-\frac{{{x}^{2}}}{2}=\frac{\pi x-{{x}^{2}}}{2}\].


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