Properties of Antiderivatives
Antiderivative of a function has various properties and the important properties of Antiderivative are,
- ∫-f(x)dx = -∫f(x)dx
- ∫ f(x) dx = ∫g(x) dx if ∫[f(x) – g(x)]dx = 0
- ∫ [k1f1(x) + k2f2(x) + …+knfn(x)]dx = k1∫ f1(x)dx + k2∫ f2(x)dx + … + kn∫ fn(x)dx
Antiderivatives
Antiderivatives: The Antiderivative of a function is the inverse of the derivative of the function. Antiderivative is also called the Integral of a function. Suppose the derivative of a function d/dx[f(x)] is F(x) + C then the antiderivative of [F(x) + C] dx of the F(x) + C is f(x). An example explains this if d/dx(sin x) is cos x then, the antiderivative of cos x, given as ∫(cos x) dx is sin x.
Antiderivative of any function is used for various purposes, to give the area of the curve, to find the volume of any 3-D curve, and others. In this article, we will learn about, Antiderivatives, Antiderivatives Formulas, Antiderivatives rules, and others in detail.
Table of Content
- What are Antiderivatives?
- Rules of Antiderivative
- Properties of Antiderivatives
- Antiderivatives Formulas
- Calculation of Antiderivative of a Function
- Antiderivative of Trigonometric Functions
- Antiderivative of Inverse Trig Functions
- Examples on Antiderivatives
- Antiderivatives Worksheet
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