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JEE Main & Advanced Sample Paper JEE Main Sample Paper-14

  • question_answer
    The slope of the tangent to the curve \[y=f(x)\] at \[(x,\,\,f(x))\] is \[2x+1\]. If the curve passes through the point (1,2) and the area of the region bounded by the curve, the x-axis and the line \[x=1\] is k sq units, then 6k is equal to

    A)  4                                            

    B)  5                 

    C)  7                                            

    D)  8         

    Correct Answer: B

    Solution :

     We have, \[\frac{dy}{dx}=2x+1\] \[\Rightarrow \] \[y={{x}^{2}}+x+C,\] which will pass through (1, 2) \[\therefore \]  \[2=1+1+C\Rightarrow \,C=0\] \[\therefore \]  \[y={{x}^{2}}+\,x\] Is the required curve \[\therefore \] Required area \[=\int_{0}^{1}{({{x}^{2}}+x)\,dx}\] \[=\left[ \frac{{{x}^{3}}}{3}+\frac{{{x}^{2}}}{2} \right]_{0}^{1}\] \[\Rightarrow \]               \[\frac{5}{6}=k\] \[\Rightarrow \]               \[6k=5\]


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