INTRODUCTION TO THE INTEGRAL COURSE ✅ INTEGRAL INDEFINITE #01
How do you calculate the indefinite integral?
INTRODUCTION TO THE INTEGRAL COURSE | ANTIDERIVATIVE
The process of calculating the integral of a function is called integration. The indefinite integral is also known as the antiderivative.
Indefinite integrals
Like addition and subtraction, multiplication and division, the inverse operation of differentiation is the antiderivation or indefinite integration.
Given a function g(x), any function f'(x) such that f'(x) = g(x) is called the indefinite integral or antiderivative of f(x).
Examples:
If f(x) = x^4 , then is the derivative of f(x). One of the antiderivatives of f'(x) = g(x) = x^4 is .
If f(x) = x^3, then f'(x) = 3x^2 = g(x). One of the antiderivatives or indefinite integrals of g(x) = 3x^2 is f(x) = x^3.
If f(x) = x^3 + 4, then f'(x) = 3x^2 = g(x). One of the antiderivatives or indefinite integrals of g(x) = 3x^2 is f(x) = x^3 + 4.
In examples 2 and 3 we can see that both x3 and x^3+4 are indefinite integrals for 3x^2. The difference between any of these functions (called primitive functions) is always a constant, that is, the indefinite integral of 3x^2 is x^3+C, where C is a real constant.
What is the indefinite integral?
The indefinite integral is one that has no intervals of integration and therefore does not represent the area under a curve.
How to calculate integrals?
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