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??

Printable View

- Jun 20th 2012, 01:53 AMcooper607integration 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??* - Jun 20th 2012, 02:29 AMsimamuraRe: integration constant
Summation is equivalent to definite integral. In definite integral we don't need constant.

- Jun 20th 2012, 09:00 AMrichard1234Re: integration constant
Consider the indefinite integral

$\displaystyle \int x^2 \, dx$

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

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