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JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    Direction: (Q. Nos. 85) Let \[\frac{dy}{dx}=\frac{1}{x+y}\,\] and \[y(0)=0\]. Then
    \[\int\limits_{0}^{1}{x\,dx}\] is equal to

    A)  \[\frac{1}{2}\]                                  

    B)  \[\frac{e}{2}\]

    C)  \[e-\frac{1}{2}\]                             

    D)  \[e-\frac{5}{2}\]

    Correct Answer: D

    Solution :

     \[\int_{0}^{1}{x\,\,dy}=\,\int_{0}^{1}{({{e}^{y}}-y-1)\,dy}\] \[=\left( {{e}^{y}}-\frac{{{y}^{2}}}{2}-y \right)_{0}^{1}\] \[=e-\frac{5}{2}\]


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