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  2. List of definite integrals - Wikipedia

    en.wikipedia.org/wiki/List_of_definite_integrals

    In mathematics, the definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} is the area of the region in the xy -plane bounded by the graph of f , the x -axis, and the lines x = a and x = b , such that area above the x -axis adds to the total, and that below the x -axis subtracts from the total.

  3. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    A. Dieckmann, Table of Integrals (Elliptic Functions, Square Roots, Inverse Tangents and More Exotic Functions): Indefinite Integrals Definite Integrals; Math Major: A Table of Integrals; O'Brien, Francis J. Jr. "500 Integrals of Elementary and Special Functions". Derived integrals of exponential, logarithmic functions and special functions.

  4. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [5] It is known in Russia as the universal trigonometric substitution , [ 6 ] and also known by variant names such as half-tangent substitution or half-angle substitution .

  5. List of integrals of exponential functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023.

  6. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    A definite integral of a function can be represented as the signed area of the region bounded by its graph and the horizontal axis; in the above graph as an example, the integral of () is the yellow (−) area subtracted from the blue (+) area

  7. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    Thus, the integral of the velocity function (the derivative of position) computes how far the car has traveled (the net change in position). The first fundamental theorem says that the value of any function is the rate of change (the derivative) of its integral from a fixed starting point up to any chosen end point.

  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. List of integrals of rational functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    The following is a list of integrals (antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form:

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