Integraalikonstant

Integraalikonstant, often denoted by the letter C, is a term that arises in indefinite integration. When finding the indefinite integral of a function, say f(x), the result is not a single function but rather a family of functions that differ by a constant. This constant is known as the integraalikonstant.

The reason for its existence lies in the fact that the derivative of any constant is zero. Therefore, if F(x) is an antiderivative of f(x), meaning F'(x) = f(x), then F(x) + C, where C is any real number, is also an antiderivative because the derivative of (F(x) + C) is F'(x) + 0 = f(x). The indefinite integral of f(x) is then written as ∫f(x) dx = F(x) + C.

The integraalikonstant represents the ambiguity inherent in reversing the differentiation process. Without additional information, such as an initial condition (a specific point the antiderivative must pass through), it is impossible to determine the exact value of C. For definite integrals, however, the integraalikonstant cancels out when evaluating the difference between the upper and lower limits of integration, and thus it does not appear in the final result.