integration constant question

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):

[tex] f' = \frac{1}{2}(\phi'+\frac{\psi}{c}) [/tex]

Integrating:

[tex] f(s) = \frac{1}{2}\phi(s) + \frac{1}{2c}\int_0^s\psi + A [/tex]

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.