integration constant

**cooper607** · June 20th 2012, 01:53 AM

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??

**simamura** · June 20th 2012, 02:29 AM

Summation is equivalent to definite integral. In definite integral we don't need constant.

**richard1234** · June 20th 2012, 09:00 AM

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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