JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

  • question_answer
    The area of the region (in sq. units), in the first quadrant, bounded by the parabola \[y=9{{x}^{2}}\] and the lines \[x=0,\] \[y=1\] and \[y=4\] is:     JEE Main  Online Paper (Held On 22 April 2013)

    A)  \[7/9\]                  

    B)  \[14/3\]

    C)  \[7/3\]                                  

    D)  \[14/9\]

    Correct Answer: D

    Solution :

     Required area \[=\int\limits_{y\,=\,1}^{4}{\sqrt{\frac{y}{9}}dy}\] \[=\frac{1}{3}\left. \int\limits_{y\,=\,1}^{4}{{{y}^{1/2}}dy=\frac{1}{3}\times \frac{2}{3}({{y}^{3/2}})} \right|_{1}^{4}\]                 \[=\frac{2}{9}[{{({{4}^{1/2}})}^{3}}-{{({{1}^{1/2}})}^{3}}]=\frac{2}{9}[8-1]\] \[=\frac{2}{9}\times 7=\frac{14}{9}\]sq. units

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