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 \[y=-{{x}^{2}}+2x+3\]and\[y=0\] is                                                                       [Orissa JEE 2004]

    A)            \[32\]                                      

    B)            \[\frac{32}{3}\]

    C)            \[\frac{1}{32}\]                   

    D)            \[\frac{1}{3}\]

    Correct Answer: B

    Solution :

               Given, \[y=-{{x}^{2}}+2x+3\]and \[y=0\]                    Therefore, \[x=-1\] and \[x=3\]                    \ Required area \[=\int_{-1}^{3}{(-{{x}^{2}}+2x+3)dx}\]                                                                        \[=\left[ -\frac{{{x}^{3}}}{3}+{{x}^{2}}+3x \right]_{-1}^{3}=\frac{32}{3}\].

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