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  2. J-integral - Wikipedia

    en.wikipedia.org/wiki/J-integral

    The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.

  3. Template:Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Template:Lists_of_integrals

    Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide This page was last edited on 4 April 2024, at 01:26 ...

  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. Category:Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Category:Lists_of_integrals

    Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help Pages in category "Lists of integrals" The following 11 pages are in this ...

  6. File:Integral approximations J.svg - Wikipedia

    en.wikipedia.org/wiki/File:Integral...

    You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses ...

  7. James R. Rice - Wikipedia

    en.wikipedia.org/wiki/James_R._Rice

    A path independent integral and the approximate analysis of strain concentration by notches and cracks. Department of Defense Advanced Research Projects Agency. Contract SD-86, Material Research Program, May 1967. Rice, James R. "Mathematical analysis in the mechanics of fracture." Fracture: an advanced treatise 2 (1968): 191–311.

  8. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    This visualization also explains why integration by parts may help find the integral of an inverse function f −1 (x) when the integral of the function f(x) is known. Indeed, the functions x(y) and y(x) are inverses, and the integral ∫ x dy may be calculated as above from knowing the integral ∫ y dx.

  9. Gradshteyn and Ryzhik - Wikipedia

    en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

    Gradshteyn and Ryzhik (GR) is the informal name of a comprehensive table of integrals originally compiled by the Russian mathematicians I. S. Gradshteyn and I. M. Ryzhik. . Its full title today is Table of Integrals, Series, and Produ

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