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JEE Main & Advanced Mathematics Definite Integration Question Bank Self Evaluation Test - Application of Integrals

  • 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:

    A) 7/9

    B) 14/3

    C) 7/3

    D) 14/9

    Correct Answer: D

    Solution :

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


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