# Math Help - integration constant

1. ## 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??

2. ## Re: integration constant

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

3. ## 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.