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  2. Power rule - Wikipedia

    en.wikipedia.org/wiki/Power_rule

    With hindsight, however, it is considered the first general theorem of calculus to be discovered. [1] The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse ...

  3. List of calculus topics - Wikipedia

    en.wikipedia.org/wiki/List_of_calculus_topics

    Constant factor rule in integration; Linearity of integration; Arbitrary constant of integration; Cavalieri's quadrature formula; Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution ...

  4. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    In integral calculus, integration by reduction formulae is a method relying on recurrence relations. It is used when an expression containing an integer parameter , usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree , can't be integrated directly.

  5. 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.

  6. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    The most general power rule is the functional power rule: ... Differential of a function – Notion in calculus; Differentiation of integrals – Problem in mathematics;

  7. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    Differential calculus and integral calculus are connected by the fundamental theorem of calculus. ... This is known as the power rule. For example, ...

  8. 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.

  9. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    Integration by parts can be extended to functions of several variables by applying a version of the fundamental theorem of calculus to an appropriate product rule. There are several such pairings possible in multivariate calculus, involving a scalar-valued function u and vector-valued function (vector field) V .

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