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

  • question_answer The area of the region bounded by the curve \[y=x|x|\],       x-axis and the ordinates \[x=1,\,\,x=-1\]is given by [Pb. CET 2004]

    A)            Zero                                         

    B)  \[\frac{1}{3}\]

    C)            \[\frac{2}{3}\]                      

    D)            1

    Correct Answer: C

    Solution :

               Required area \[=\int_{-1}^{1}{x|x|dx}\]\[=\int_{-1}^{0}{-{{x}^{2}}dx+\int_{0}^{1}{{{x}^{2}}dx}}\]                                           =\[\left( \frac{-{{x}^{3}}}{3} \right)_{-1}^{0}\]\[+\left( \frac{{{x}^{3}}}{3} \right)_{0}^{1}\]\[=\left| \,\frac{-1}{3}\, \right|+\left| \,\frac{1}{3}\, \right|=\frac{2}{3}\].

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