Integral from a to c of f(x): Understanding the Fundamentals and Calculation Method

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To find the integral from a to c of f(x) with respect to x, we first need to find the antiderivative or the indefinite integral of f(x)

To find the integral from a to c of f(x) with respect to x, we first need to find the antiderivative or the indefinite integral of f(x). Let’s assume F(x) represents the antiderivative of f(x).

The definite integral from a to c of f(x) can be written as:

∫[a to c] f(x) dx

Using the second fundamental theorem of calculus, which states that the definite integral of a function can be evaluated using its antiderivative, we have:

∫[a to c] f(x) dx = F(c) – F(a)

This means that the definite integral of f(x) from a to c is equal to the difference between the antiderivative of f(x) evaluated at c and the antiderivative evaluated at a.

In summary,

∫[a to c] f(x) dx = F(c) – F(a)

More Answers:

Understanding the Fundamental Theorem of Calculus: A Guide to Evaluating Definite Integrals
Mastering the Indefinite Integral: Fundamentals, Techniques, and Applications in Calculus
Understanding the Zero Width Integral: Exploring the Integral from a to a of f(x) in Mathematics

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