In this lesson, we introduce a notation for antiderivatives called the Indefinite Integral. We will also give a list of integration formulas that would be useful to know.
The notation is used for an antiderivative of f and is called the indefinite integral.
The following is a table of formulas of the commonly used Indefinite Integrals. You can verify any of the formulas by differentiating the function on the right side and obtaining the integrand.
Find the general indefinite integral
The connection between the definite integral and indefinite integral is given by the second part of the Fundamental Theorem of Calculus.
If f is continuous on [a, b] then
Take note that a definite integral is a number, whereas an indefinite integral is a function.
Definition of Indefinite Integrals
An indefinite integral is a function that takes the antiderivative of another function. It is visually represented as an integral symbol, a function, and then a dx at the end. The indefinite integral is an easier way to symbolize taking the antiderivative. The indefinite integral is related to the definite integral, but the two are not the same.
Antiderivatives and indefinite integrals
Indefinite integrals are functions that do the opposite of what derivatives do. They represent taking the antiderivatives of functions. A formula useful for solving indefinite integrals is that the integral of x to the nth power is one divided by n+1 times x to the n+1 power, all plus a constant term.
Indefinite integrals, step by step, examples.
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