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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    \[\int_{0}^{\pi /2}{x\,\sin \,x}\,\,dx\]is equal to

    A)  \[0\]

    B)  \[1\]

    C)  \[-1\]

    D)  \[2\]

    Correct Answer: B

    Solution :

    \[\int_{0}^{\pi /2}{x\,\sin \,x\,dx=[x(-\cos x)]_{0}^{\pi /2}}\] \[-\int_{0}^{\pi /2}{1\,(-\cos \,x)dx}\] \[=\left[ -\frac{\pi }{2}\,\cos \frac{\pi }{2}-0 \right]+[\operatorname{six}\,x]_{0}^{\pi /2}\] \[=0+1-0=1\]


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