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A function F(x) is an h-antiderivative of f(x) if D h F(x) = f(x).The h-integral is denoted by ().If a and b differ by an integer multiple of h then the definite integral () is given by a Riemann sum of f(x) on the interval [a, b], partitioned into sub-intervals of equal width h.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
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.
Sums are over the discrete variable s z, integrals over continuous positions r. For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is mathematically necessary). Following are general mathematical results, used in calculations.
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 ...
However, this formal similarity notwithstanding, possessing a complex-antiderivative is a much more restrictive condition than its real counterpart. While it is possible for a discontinuous real function to have an anti-derivative, anti-derivatives can fail to exist even for holomorphic functions of a complex variable.
The q-derivative of a function f(x) is defined as [1] [2] [3] () = ().It is also often written as ().The q-derivative is also known as the Jackson derivative.. Formally, in terms of Lagrange's shift operator in logarithmic variables, it amounts to the operator
Equation solver (root finder) that can solve for any variable in an equation; Numerical integration for calculating definite integrals; Matrix operations (including a matrix editor, dot product, cross product and solver for simultaneous linear equations) Complex numbers (including polar coordinates representation) Vector functions