Math Help - integrals and constants

1. integrals and constants

can someone explain why constants dont effect integrals? Isnt the integral of a constant the constant with an x after it ? : integral of 2 should be 2x, right? or wrong? why is this so?

like the integral of 1/sqrt(2) * Dtheyta = 1/sqrt(2) * theyta (Dtheyta = derivitaive of theyta)

2. Originally Posted by frankinaround
can someone explain why constants dont effect integrals? Isnt the integral of a constant the constant with an x after it ? : integral of 2 should be 2x, right? or wrong? why is this so?

like the integral of 1/sqrt(2) * Dtheyta = 1/sqrt(2) * theyta (Dtheyta = derivitaive of theyta)
What do you mean by "constants don't effect integrals"? Unless you have some unusual meaning, they certainly do. If f(x)= g(x)+ C, then $\int f(x)dx= \int g(x)+ Cx$. That is, if f and g differ by the added constant, C, then their integrals differ by Cx.

Perhaps you are mis-remembering that an added constant does not change the derivative. If f(x)= g(x)+ C, then $\frac{df}{dx}= \frac{dg}{dx}$.

Or are you refering to the "constant of integration"? Because an added constant does not change the derivative, $\int a d\theta= a\theta+ C$ where C can be any number because $d(a\theta+ C)/d\theta= a$ for any C.