integratsiooniväärtus

Integratsiooniväärtus, often translated as integration value or integration constant, is a fundamental concept in integral calculus. It arises when performing an indefinite integration of a function. When one finds the antiderivative of a function, there is an inherent ambiguity because the derivative of a constant is always zero. Consequently, any constant can be added to a particular antiderivative, and the result will still have the same derivative. This arbitrary constant is represented by the symbol 'C' and is referred to as the integration constant.

For example, the indefinite integral of 2x is x² + C. While the derivative of x² is 2x, the derivative of x² + 1, x² + 5, or indeed x² + any_number is also 2x. Therefore, to encompass all possible antiderivatives of a given function, the integration constant 'C' is appended. In definite integration, where the integral is evaluated between two limits, the integration constant cancels out, and thus it does not appear in the final numerical result. However, it remains a crucial part of the process when dealing with indefinite integrals and solving differential equations. Understanding the role of the integration constant is essential for correctly applying integral calculus in various fields of science and engineering.