Rules of Antiderivative
Vrious rules that are used to easily solve problems of Antiderivaties are,
Constant Rule
∫kf(x)dx = k ∫ f(x)dx, here “k” is any constant.
Sum Rule
This rule states that the integral of sum of two functions is equal to sum of integrals of those two functions.
∫(f(x) + g(x))dx = ∫ f(x)dx + ∫g(x)dx
Difference Rule
This rule states that the integral of difference of two functions is equal to difference of integrals of those two functions.
∫(f(x) – g(x))dx = ∫ f(x)dx – ∫g(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