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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    If \[\int{f(x)\,dx=f(x)},\] then \[{{\int{\left[ f(x) \right]}}^{2}}\,\,dx\] is [DCE 2002]

    A)            \[\frac{1}{2}{{\left[ f\left( x \right) \right]}^{2}}\]

    B)            \[{{\left[ f\left( x \right) \right]}^{3}}\]

    C)            \[\frac{{{\left[ f\left( x \right) \right]}^{3}}}{3}\]

    D)   \[{{\left[ \,f\left( x \right) \right]}^{2}}\]

    Correct Answer: A

    Solution :

               Trick : Let \[f(x)={{e}^{x}},\] then\[\int{f(x)dx=f(x)}\]                    \[\therefore \,\int{{{({{e}^{x}})}^{2}}dx=\frac{{{e}^{2x}}}{2}=\frac{1}{2}{{[f(x)]}^{2}}.}\]


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