What is the chain rule for anti differentiation?
Inverse chain rule is a method of finding antiderivatives or integrals of a function by guessing the integral of that function, and then differentiating back using the chain rule.
What is the power rule in integrals?
The power rule for integrals allows us to find the indefinite (and later the definite) integrals of a variety of functions like polynomials, functions involving roots, and even some rational functions. If you can write it with an exponents, you probably can apply the power rule.
How do you find the specific antiderivative?
To find the specific antiderivative, call it f(x), of a function F(x) given the initial condition that f(a) = b, we use the following steps: Find the general antiderivative of F(x) with its constant C. Plug the initial conditions into the general antiderivative and solve for C.
What is antiderivative in simple terms?
An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a function plus an arbitrary constant. Antiderivatives are a key part of indefinite integrals.
What is power formula in integral calculus?
The General Power Formula | Fundamental Integration Formulas The General Power Formula as shown in Chapter 1 is in the form. ∫undu=un+1n+1+C;n≠−1. Thus far integration has been confined to polynomial functions.
Why does the power rule work?
The power rule is a quick tool for finding the derivative of a function. It works whenever you can write the expression so that each term is simply a variable raised to a power. The power rule works if the exponent is negative or fractional as well. It is one of the most commonly used techniques in calculus.
What are the applications of antiderivatives?
Antiderivatives and Differential Equations Antidifferentiation can be used in finding the general solution of the differential equation. Motion along a Straight Line Antidifferentiation can be used to find specific antiderivatives using initial conditions, including applications to motion along a line.