# integration constant

• June 20th 2012, 01:53 AM
cooper607
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??
• June 20th 2012, 02:29 AM
simamura
Re: integration constant
Summation is equivalent to definite integral. In definite integral we don't need constant.
• June 20th 2012, 09:00 AM
richard1234
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.