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

  • question_answer The area between the parabola \[y={{x}^{2}}\] and the line \[y=x\] is                                                     [UPSEAT 2004]

    A)            \[\frac{1}{6}\]sq. unit       

    B)            \[\frac{1}{3}\]sq. unit

    C)            \[\frac{1}{2}\]sq. unit       

    D)            None of these

    Correct Answer: A

    Solution :

               Given curves are \[y={{x}^{2}}\]and \[y=x\]                    On solving, we get \[x=0\], \[x=1\]
               Therefore, required area \[A=\int_{0}^{1}{({{x}^{2}}-x)}dx\]            \[=\left[ \frac{{{x}^{3}}}{3}-\frac{{{x}^{2}}}{2} \right]_{0}^{1}\]\[=\frac{1}{3}-\frac{1}{2}=\frac{1}{6}\] sq. unit.

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