Cambridge O Level Additional Mathematics · Syllabus 4037 · Calculus
Indefinite Integral
What is Indefinite Integral?
The family of all functions whose derivative is a given function. If F dashed of x equals f of x, then the indefinite integral of f with respect to x is written as F of x plus C, where C is an arbitrary constant. The constant is required because differentiating any constant gives zero, so infinitely many functions differing only by a constant share the same derivative, and reversing the process cannot recover which one was intended. An indefinite integral is a family of functions, not a number, and any indefinite integral can be checked by differentiating the result to see whether the original function is recovered.
This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.