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Math Help - integration constant

  1. #1
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    integration constant

    anyway let me ask something more basic...why do we have a integrational constant in calculus? if we sum ( in summation) up the thing do we need any constant like this??
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  2. #2
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    Re: integration constant

    Summation is equivalent to definite integral. In definite integral we don't need constant.
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  3. #3
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    Re: integration constant

    Consider the indefinite integral

    \int x^2 \, dx

    We can say that the anti-derivative of x^2 is \frac{x^3}{3}. However, another anti-derivative could be \frac{x^3}{3} + 1, or perhaps \frac{x^3}{3} - \pi. This is because the derivative of a constant is zero.

    To remove all this ambiguity we say that \int x^2 \, dx = \frac{x^3}{3} + C, where C is an arbitrary constant.
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