The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated...

vector calculus. In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes'...

century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton. The theorem demonstrates a connection between integration...

case of Stokes' theorem (surface in R 3 {\displaystyle \mathbb {R} ^{3}} ). In one dimension, it is equivalent to the fundamental theorem of calculus. In...

algebra Fundamental theorem of calculus Fundamental theorem of calculus for line integrals Fundamental theorem of curves Fundamental theorem of cyclic...

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...

version of the second fundamental theorem of calculus, that integrals can be computed using any of a function's antiderivatives. The first full proof of the...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree...

(by the fundamental theorem of calculus) in the framework of Riemann integration, but with absolute continuity it may be formulated in terms of Lebesgue...

decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational...

allows expressing the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general result...

function at that point. Differential calculus and integral calculus are connected by the fundamental theorem of calculus. This states that differentiation...

integration Linearity of integration Arbitrary constant of integration Cavalieri's quadrature formula Fundamental theorem of calculus Integration by parts...

accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make...

(variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation...

generalization of the product rule Leibniz integral rule The alternating series test, also called Leibniz's rule The Fundamental theorem of calculus, also called...

fundamental theorem of calculus. Laisant proved that if F {\displaystyle F} is an antiderivative of f {\displaystyle f} , then the antiderivatives of...

is now known as Rolle's theorem, and was proved only for polynomials, without the techniques of calculus. The mean value theorem in its modern form was...

of derivatives and integrals in alternative calculi List of equations List of fundamental theorems List of hypotheses List of inequalities Lists of integrals...

applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration, or simulated using...

Derivative Fundamental theorem of calculus Integral Limit Non-standard analysis Partial derivative Infinite Series Sir Isaac Newton Gottfried Leibniz List of calculus...

These two points of view are related to each other by the fundamental theorem of discrete calculus. The study of the concepts of change starts with...

related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval where the function...

in X to g(f(x)) in Z. fundamental theorem of calculus The fundamental theorem of calculus is a theorem that links the concept of differentiating a function...

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...

development of infinitesimal calculus; in particular, for proof of the fundamental theorem of calculus. His work centered on the properties of the tangent;...

(roughly speaking) measures precisely the extent to which the fundamental theorem of calculus fails in higher dimensions and on general manifolds. — Terence...

be derived using the fundamental theorem of calculus. The (first) fundamental theorem of calculus is just the particular case of the above formula where...