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 curves \[y=|x-2|,\] \[x=1,\,\,x=3\]and the x-axis is                                          [AIEEE 2004]

    A)            4    

    B)            2

    C)            3    

    D)            1

    Correct Answer: D

    Solution :

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

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