Calculus

Forgetting the Constant of Integration

Students find an indefinite integral and leave off the constant +C+ C.

Quick check

Why students make it

They focus on reversing the derivative rule and forget that many functions have the same derivative. Since constants disappear when differentiating, an antiderivative represents a whole family of functions.

The rule done right

Every indefinite integral needs a constant of integration: ∫f(x) dx=F(x)+C\int f(x)\,dx = F(x) + C when F′(x)=f(x)F'(x)=f(x). Use an initial condition, if given, to solve for CC.

Related resources

integralsantiderivativesconstant-of-integration