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 figure bounded by \[y={{e}^{x}},\,y={{e}^{-x}}\] and the straight line \[x=1\] is                                            [Karnataka CET 1999]

    A)            \[e+\frac{1}{e}\]                

    B)            \[e-3\]

    C)            \[e+\frac{1}{e}-2\]            

    D)            \[e+\frac{1}{e}+2\]

    Correct Answer: C

    Solution :

               Given equations of curves \[y={{e}^{x}};y={{e}^{-x}}\] and straight line \[x=1\] We know that area of the figure bounded by the curves and straight line                     \[=\int_{0}^{1}{({{e}^{x}}-{{e}^{-x}})dx=[{{e}^{x}}+{{e}^{-x}}]\,_{0}^{1}\,=\,e+\frac{1}{e}-2.}\]

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