Search results
Results from the WOW.Com Content Network
In mathematics, the definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} is the area of the region in the xy -plane bounded by the graph of f , the x -axis, and the lines x = a and x = b , such that area above the x -axis adds to the total, and that below the x -axis subtracts from the total.
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.
This list may not reflect recent changes. Integral * Lobachevsky integral formula; A. ... Visual calculus; Volkenborn integral; W.
The resulting integrands are of the same form as the original integrand, so these reduction formulas can be repeatedly applied to drive the exponents m and p toward 0. These reduction formulas can be used for integrands having integer and/or fractional exponents.
Indefinite integrals are antiderivative functions. A constant (the constant of integration) may be added to the right hand side of any of these formulas, but has been suppressed here in the interest of brevity.
Xcas can solve differential equations. Xcas is a user interface to Giac , which is an open source [ 2 ] computer algebra system (CAS) for Windows , macOS and Linux among many other platforms. Xcas is written in C++ . [ 3 ]
The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.
Integral equations are important in many applications. Problems in which integral equations are encountered include radiative transfer, and the oscillation of a string, membrane, or axle. Oscillation problems may also be solved as differential equations. Actuarial science (ruin theory [8]) Computational electromagnetics