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  2. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. [42] Various different line integrals are in use. In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field.

  3. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Integration is the basic operation in integral calculus. ... Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas. Russian edition, Fiziko ...

  4. Integration using Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Integration_using_Euler's...

    In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions.Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated.

  5. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    Integration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...

  6. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/.../Fundamental_theorem_of_calculus

    From the conjecture and the proof of the fundamental theorem of calculus, calculus as a unified theory of integration and differentiation is started. The first published statement and proof of a rudimentary form of the fundamental theorem, strongly geometric in character, [ 2 ] was by James Gregory (1638–1675).

  7. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. [46]: 508 The indefinite integral, also known as the antiderivative, is the inverse operation to the derivative.

  8. Trapezoidal rule - Wikipedia

    en.wikipedia.org/wiki/Trapezoidal_rule

    In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: (). The trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating its area.

  9. Gradient theorem - Wikipedia

    en.wikipedia.org/wiki/Gradient_theorem

    Now, since u'(s) = v, the limit becomes (()) ′ = (+) | = = where the first equality is from the definition of the derivative with a fact that the integral is equal to 0 at t = 0, and the second equality is from the first fundamental theorem of calculus. Thus we have a formula for ∂ v f, (one of ways to represent the directional derivative ...

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