# What is the difference between an antiderivative and an integral?

There are no differences, the two words are synonymous.

By signing up, you agree to our Terms of Service and Privacy Policy

It depends on a couple of things. Which antiderivative, the general or a particular? which integral definite or indefinite? And, who are we asking?

General Antiderivative and Indefinite Integral:

Definite integrals

(To further complicate matters, this definite integral can be found, using the Fundamental Theorem of Calculus, Part 2, by finding the/an indefinite integral / general antiderivative first, then doing somearithmetic.)

By signing up, you agree to our Terms of Service and Privacy Policy

Your question is related to what was truly the "key insight" in the development of calculus by Isaac Newton and Gottfried Leibniz.

Focusing on functions that are never negative, this insight can be phrased as: "Antiderivatives can be used to find areas (integrals) and areas (integrals) can be used to define antiderivatives". This is the essence of the Fundamental Theorem of Calculus.

By signing up, you agree to our Terms of Service and Privacy Policy

An antiderivative is a function whose derivative is equal to a given function. An integral is a mathematical operation that can be interpreted as finding the area under a curve. The relationship between antiderivatives and integrals is described by the Fundamental Theorem of Calculus, which states that integration and differentiation are inverse operations.

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you find the antiderivative of #e^(2x) * sqrt(e^x + 1)#?
- How do you use the Fundamental Theorem of Calculus to find the derivative of #int (2t - 1)^3dt# from x^5 to x^6?
- How do you find #int 1-tanx^2dx#?
- How do you find the general antiderivative of #f(x)= sin2x+cos2x#?
- What is the integral of #int (x-2)/(x-1)# from 0 to 2?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7