Indefinite integrals
Find antiderivatives by reversing differentiation and explain the constant of integration.
Meaning
An indefinite integral represents the antiderivatives whose derivative is the given function. Antiderivatives with the same derivative on the same interval differ by a constant. The derivative of the difference of two antiderivatives is zero. On the same interval, the mean value theorem makes a function with zero derivative constant, so the difference is a constant.
Example
Practice for this concept
Scope and references
Topics
Antiderivatives, constants of integration, basic integration formulas
Learning goal
Find antiderivatives by reversing differentiation and explain the constant of integration.
Helpful background
Check which function a derivative produces and the derivative of a constant.
Indefinite integrals
These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.