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

  • question_answer The area bounded by the curve \[y={{x}^{3}},\] \[x-\]axis and two ordinates \[x=1\] to \[x=2\] equal to                [MP PET 1999]

    A)            \[\frac{15}{2}\] sq. unit   

    B)            \[\frac{15}{4}\] sq. unit

    C)            \[\frac{17}{2}\] sq. unit   

    D)            \[\frac{17}{4}\] sq. unit

    Correct Answer: B

    Solution :

                       Shaded area \[=\int_{1}^{2}{y\,dx}\]\[=\int_{1}^{2}{{{x}^{3}}.dx=\frac{1}{4}[{{x}^{4}}]_{1}^{2}}\]                    \[A=\frac{1}{4}[16-1]=\frac{15}{4}\] sq. unit.


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