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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    If \[f'(x)={{x}^{2}}+5\] and \[f(0)=-1\], then \[f(x)=\]

    A)            \[{{x}^{3}}+5x-1\]

    B)            \[{{x}^{3}}+5x+1\]

    C)            \[\frac{1}{3}{{x}^{3}}+5x-1\]

    D)            \[\frac{1}{3}{{x}^{3}}+5x+1\]

    Correct Answer: C

    Solution :

               Given that \[{f}'(x)={{x}^{2}}+5\] and \[f(0)=-1\]            Þ \[f(x)=\frac{{{x}^{3}}}{3}+5x+c\]. If \[x=0,\] then \[f(0)=c\]Þ \[c=-1\].            Hence \[f(x)=\frac{{{x}^{3}}}{3}+5x-1.\]


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