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  2. Volume integral - Wikipedia

    en.wikipedia.org/wiki/Volume_integral

    In mathematics (particularly multivariable calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass from a corresponding density ...

  3. Multiple integral - Wikipedia

    en.wikipedia.org/wiki/Multiple_integral

    Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. [1]

  4. Shell integration - Wikipedia

    en.wikipedia.org/wiki/Shell_integration

    Much more work is needed to find the volume if we use disc integration. First, we would need to solve y = 8 ( x − 1 ) 2 ( x − 2 ) 2 {\displaystyle y=8(x-1)^{2}(x-2)^{2}} for x . Next, because the volume is hollow in the middle, we would need two functions: one that defined an outer solid and one that defined the inner hollow.

  5. Finite volume method - Wikipedia

    en.wikipedia.org/wiki/Finite_volume_method

    The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. [1] In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then ...

  6. Direct comparison test - Wikipedia

    en.wikipedia.org/wiki/Direct_comparison_test

    In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing whether an infinite series or an improper integral converges or diverges by comparing the series or integral to one whose convergence properties are known.

  7. Disc integration - Wikipedia

    en.wikipedia.org/wiki/Disc_integration

    Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution. This method models the resulting three-dimensional shape as a stack of an infinite number of discs of varying radius ...

  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 is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...