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  2. Institutiones calculi integralis - Wikipedia

    en.wikipedia.org/wiki/Institutiones_calculi...

    Institutiones calculi integralis (Foundations of integral calculus) is a three-volume textbook written by Leonhard Euler and published in 1768. It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations .

  3. Glasser's master theorem - Wikipedia

    en.wikipedia.org/wiki/Glasser's_master_theorem

    In integral calculus, Glasser's master theorem explains how a certain broad class of substitutions can simplify certain integrals over the whole interval from to +. It is applicable in cases where the integrals must be construed as Cauchy principal values, and a fortiori it is applicable when the integral converges absolutely.

  4. Bioche's rules - Wikipedia

    en.wikipedia.org/wiki/Bioche's_rules

    These rules can be, in fact, stated as a theorem: one shows [1] that the proposed change of variable reduces (if the rule applies and if f is actually of the form () = (⁡, ⁡) (⁡, ⁡)) to the integration of a rational function in a new variable, which can be calculated by partial fraction decomposition.

  5. Calculus Made Easy - Wikipedia

    en.wikipedia.org/wiki/Calculus_Made_Easy

    Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis.

  6. 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.

  7. 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.

  8. Nonstandard analysis - Wikipedia

    en.wikipedia.org/wiki/Nonstandard_analysis

    Download as PDF; Printable version; ... stages of the Differential and Integral Calculus. ... simplified approach is also more suitable for use by mathematicians who ...

  9. 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.

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