Understanding Integration Constants: Debunking Common Misconceptions

[wumple]

Hi,

I thought that if you integrate with limits, you don't include a constant, but if you don't integrate with limits (indefinite), there is a constant. But my book gives the example (all functions are single variable functions, initially of x but then changed to s for the integration):

$$f' = \frac{1}{2}(\phi'+\frac{\psi}{c})$$

Integrating:

$$f(s) = \frac{1}{2}\phi(s) + \frac{1}{2c}\int_0^s\psi + A$$

What's going on here?

 

[mathwonk]

the first statement implies the second. I.e. if all you know about f is its derivative, then you can only know f up to an additive constant.

try to get away from memorizing mindless rules like the (flawed) ones you stated. learn what the concepts mean.