Search results
Results from the WOW.Com Content Network
The graphs of antiderivatives of a given function are vertical translations of each other, with each graph's vertical location depending upon the value c. More generally, the power function has antiderivative if n ≠ −1, and if n = −1. In physics, the integration of acceleration yields velocity plus a constant.
Integration by substitution. In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [ 1 ] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards."
Constant of integration. In calculus, the constant of integration, often denoted by (or ), is a constant term added to an antiderivative of a function to indicate that the indefinite integral of (i.e., the set of all antiderivatives of ), on a connected domain, is only defined up to an additive constant. [1][2][3] This constant expresses an ...
Calculus. In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative.
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...
Nonelementary integral. In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field ...
Miscellanea. v. t. e. In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse of a continuous and invertible function , in terms of and an antiderivative of . This formula was published in 1905 by Charles-Ange Laisant. [1]
The following is a list of integrals ( antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form: , and. which can then be integrated term by term. For other types of functions, see lists of integrals . Miscellaneous integrands.