In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle...

space. The transformed function can generally be mapped back to the original function space using the inverse transform. An integral transform is any transform...

of functions (the measurable functions) this defines the Lebesgue integral. A general measurable function f is Lebesgue-integrable if the sum of the...

see lists of integrals. The inverse trigonometric functions are also known as the "arc functions". C is used for the arbitrary constant of integration...

mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and...

the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric...

antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a continuous function f is a differentiable function F whose...

is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas...

of integrals of inverse trigonometric functions List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals...

antiderivative, is the inverse operation to the derivative.: 163–165  F is an indefinite integral of f when f is a derivative of F. (This use of lower- and upper-case...

List of integrals of irrational functions List of integrals of trigonometric functions List of integrals of inverse trigonometric functions List of integrals...

mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear...

mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in...

defines integrals for a class of functions called measurable functions. A real-valued function f on E is measurable if the pre-image of every interval of the...

versions of the inverse function theorem for holomorphic functions, for differentiable maps between manifolds, for differentiable functions between Banach...

In mathematics, the inverse Laplace transform of a function F ( s ) {\displaystyle F(s)} is a real function f ( t ) {\displaystyle f(t)} that is piecewise-continuous...

more variables, a multiple integral will yield hypervolumes of multidimensional functions. Multiple integration of a function in n variables: f(x1, x2,...

integral analogue of the line integral. Given a surface, one may integrate over this surface a scalar field (that is, a function of position which returns a...

such as matrices, or power functions. A standard course considers functions, function composition, and inverse functions, often in connection with sets...

applications. The definite integral of the secant function starting from 0 {\displaystyle 0} is the inverse Gudermannian function, gd − 1 . {\textstyle \operatorname...

calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially...

calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative...

type of implicit function is an inverse function. Not all functions have a unique inverse function. If g is a function of x that has a unique inverse, then...

The inverse tangent integral is a special function, defined by: Ti 2 ⁡ ( x ) = ∫ 0 x arctan ⁡ t t d t {\displaystyle \operatorname {Ti} _{2}(x)=\int _{0}^{x}{\frac...

multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does so...

until 1868. For many functions and practical applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated...

of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced by the non-nullity of the Jacobian...

functions: The inverses of elliptic integrals; used to model double-periodic phenomena. Jacobi's elliptic functions Weierstrass's elliptic functions Lemniscate...

known as u-substitution, reverse chain rule or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the...

several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the...