Search results
Results From The WOW.Com Content Network
Some common non-elementary antiderivative functions are given names, defining so-called special functions, and formulas involving these new functions can express a larger class of non-elementary antiderivatives. The examples above name the corresponding special functions in parentheses.
Nonelementary integral – Integrals not expressible in closed-form from elementary functions; Risch algorithm – Method for evaluating indefinite integrals; Tarski's high school algebra problem – Mathematical problem; Transcendental function – Analytic function that does not satisfy a polynomial equation
Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. [46]: 508 The indefinite integral, also known as the antiderivative, is the inverse operation to the derivative.
Risch called it a decision procedure, because it is a method for deciding whether a function has an elementary function as an indefinite integral, and if it does, for determining that indefinite integral. However, the algorithm does not always succeed in identifying whether or not the antiderivative of a given function in fact can be expressed ...
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).
“In some cases, the integral from a to c is not even defined, because the integrals of the positive and negative parts of f(x) dx from a to c are both infinite, but nonetheless the limit may exist. Such cases are "properly improper" integrals, i.e. their values cannot be defined except as such limits.