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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. Simpson's rule - Wikipedia

    en.wikipedia.org/wiki/Simpson's_rule

    Composite Simpson's 3/8 rule is even less accurate. Integration by Simpson's 1/3 rule can be represented as a weighted average with 2/3 of the value coming from integration by the trapezoidal rule with step h and 1/3 of the value coming from integration by the rectangle rule with step 2h. The accuracy is governed by the second (2h step) term.

  4. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.

  5. Gradshteyn and Ryzhik - Wikipedia

    en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

    In 1995, Alan Jeffrey published his Handbook of Mathematical Formulas and Integrals. [22] It was partially based on the fifth English edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and meant as an companion, but written to be more accessible for students and practitioners. [22] It went through four editions up to 2008.

  6. Cavalieri's quadrature formula - Wikipedia

    en.wikipedia.org/wiki/Cavalieri's_quadrature_formula

    For negative values of n (negative powers of x), there is a singularity at x = 0, and thus the definite integral is based at 1, rather than 0, yielding: = + (+) Further, for negative fractional (non-integer) values of n, the power x n is not well-defined, hence the indefinite integral is only defined for positive x.

  7. English grammar - Wikipedia

    en.wikipedia.org/wiki/English_grammar

    The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...

  8. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    the integral is called an indefinite integral, which represents a class of functions (the antiderivative) whose derivative is the integrand. [19] The fundamental theorem of calculus relates the evaluation of definite integrals to indefinite integrals. There are several extensions of the notation for integrals to encompass integration on ...

  9. 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.

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