AP Calculus AB and BC glossary

Constant of integration

Also called: Plus C

The constant of integration is the arbitrary constant added to an indefinite integral. It is required because differentiating any constant gives zero, so a function has infinitely many antiderivatives that differ only by a constant.

It stops being arbitrary the moment you have an initial condition. In a differential equation, substituting a known point determines the constant and turns the general solution into a particular one.

Not needed for definite integrals

In a definite integral the constant cancels when you subtract the two endpoint values, which is why it never appears in the final answer there.

Appears in: Unit 6: Integration and Accumulation, Unit 7: Differential Equations