Antiderivative vs Integral: What is the Difference?

In calculus, the terms "antiderivative" and "integral" are often used interchangeably, which can cause confusion. While they are deeply related by the Fundamental Theorem of Calculus, they refer to slightly different mathematical concepts.

What is an Antiderivative?

An antiderivative is simply a function whose derivative is the original function you started with. It is the direct opposite of differentiation. For example, 2x is the derivative of x^2, so x^2 is an antiderivative of 2x.

What is an Integral?

The term "integral" usually refers to two different things:

• Indefinite Integrals: This represents the entire family of all possible antiderivatives for a function, which is why we add the constant of integration (+ C).
• Definite Integrals: This evaluates the net area under a curve between two specific points (limits of integration). The result is a single number, not a function.

If you need to evaluate an indefinite integral and find the family of functions, check out our Antiderivative Calculator.