integraalreegleid

Integraalreegleid, meaning "integral rules" in Estonian, refers to a set of fundamental principles and techniques used in calculus to evaluate definite and indefinite integrals. These rules are essential for understanding and applying integration, the process of finding the antiderivative of a function.

The most basic integral rule is the power rule, which states that the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where n is any real number except -1, and C is the constant of integration. Another important rule is the constant multiple rule, which allows factoring out a constant from the integral: the integral of c*f(x) dx is c times the integral of f(x) dx. The sum and difference rules permit integrating sums or differences of functions by integrating each term separately.

Other key integraalreegleid include the integral of trigonometric functions, exponential functions, and logarithmic functions. Techniques like integration by substitution, integration by parts, and partial fraction decomposition are more advanced methods used to solve integrals that cannot be solved by the basic rules alone. These rules and techniques form the bedrock of integral calculus, enabling the calculation of areas under curves, volumes of solids, and solutions to various differential equations across many scientific and engineering disciplines.