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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.
If the function f does not have any continuous antiderivative which takes the value zero at the zeros of f (this is the case for the sine and the cosine functions), then sgn(f(x)) ∫ f(x) dx is an antiderivative of f on every interval on which f is not zero, but may be discontinuous at the points where f(x) = 0.
An antiderivative, primitive function, primitive integral or indefinite integral [Note 1] of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F ′ = f {\displaystyle F'=f} .
Nonelementary antiderivatives can often be evaluated using Taylor series. Even if a function has no elementary antiderivative, its Taylor series can always be integrated term-by-term like a polynomial, giving the antiderivative function as a Taylor series with the same radius of convergence. However, even if the integrand has a convergent ...
Symbol Name Meaning SI unit of measure nabla dot : the divergence operator often pronounced "del dot" per meter (m −1) : nabla cross : the curl operator often pronounced "del cross"
There are many alternatives to the classical calculus of Newton and Leibniz; for example, each of the infinitely many non-Newtonian calculi. [1] Occasionally an alternative calculus is more suited than the classical calculus for expressing a given scientific or mathematical idea.
Later authors have assigned them other meanings, such as infinitesimals in non-standard analysis, or exterior derivatives. Commonly, dx is left undefined or equated with , while dy is assigned a meaning in terms of dx, via the equation =, which may also be written, e.g.
Integrals and derivatives of displacement, including absement, as well as integrals and derivatives of energy, including actergy. (Janzen et al. 2014) In kinematics, absement (or absition) is a measure of sustained displacement of an object from its initial position, i.e. a measure of how far away and for how long.