JEE Main & Advanced Mathematics Definite Integration Question Bank Area Bounded by Region, Volume and Surface Area of Solids of Revolution

  • question_answer Area under the curve \[y={{x}^{2}}-4x\]within the x-axis and the line \[x=2\], is                                                [SCRA 1991]

    A)            \[\frac{16}{3}sq.\,unit\]  

    B)            \[-\frac{16}{3}sq.\,unit\]

    C)            \[\frac{4}{7}sq.\,unit\]    

    D)            Cannot be calculated

    Correct Answer: A

    Solution :

               \[\int_{0}^{2}{({{x}^{2}}-4x)dx=\left[ \frac{{{x}^{3}}}{3}-\frac{4{{x}^{2}}}{2} \right]_{0}^{2}=\frac{16}{3}sq.}\]unit.

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