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  2. Riemann sum - Wikipedia

    en.wikipedia.org/wiki/Riemann_sum

    While not derived as a Riemann sum, taking the average of the left and right Riemann sums is the trapezoidal rule and gives a trapezoidal sum. It is one of the simplest of a very general way of approximating integrals using weighted averages. This is followed in complexity by Simpson's rule and Newton–Cotes formulas.

  3. File:Riemann sum convergence.svg - Wikipedia

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

    Download QR code; In other projects Appearance. move to sidebar hide ... Show convergence of Riemann sum for all sample position choices as intervals shrink.

  4. File:Polar coordinates integration Riemann sum.svg - Wikipedia

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

    The following other wikis use this file: Usage on af.wikipedia.org Poolkoördinatestelsel; Usage on ast.wikipedia.org Coordenaes polares; Usage on ba.wikipedia.org

  5. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    The Weyl tensor has the same basic symmetries as the Riemann tensor, but its 'analogue' of the Ricci tensor is zero: = = = = The Ricci tensor, the Einstein tensor, and the traceless Ricci tensor are symmetric 2-tensors:

  6. Riemann integral - Wikipedia

    en.wikipedia.org/wiki/Riemann_integral

    One popular restriction is the use of "left-hand" and "right-hand" Riemann sums. In a left-hand Riemann sum, t i = x i for all i, and in a right-hand Riemann sum, t i = x i + 1 for all i. Alone this restriction does not impose a problem: we can refine any partition in a way that makes it a left-hand or right-hand sum by subdividing it at each t i.

  7. McShane integral - Wikipedia

    en.wikipedia.org/wiki/McShane_integral

    This fact enables to conclude that with the McShane integral one formulates a kind of unification of the integration theory around Riemann sums, which, after all, constitute the origin of that theory. So far is not known an immediate proof of such theorem.

  8. Partition of an interval - Wikipedia

    en.wikipedia.org/wiki/Partition_of_an_interval

    A partition of an interval being used in a Riemann sum. The partition itself is shown in grey at the bottom, with the norm of the partition indicated in red. In mathematics, a partition of an interval [a, b] on the real line is a finite sequence x 0, x 1, x 2, …, x n of real numbers such that a = x 0 < x 1 < x 2 < … < x n = b.

  9. File:Riemann sum error.svg - Wikipedia

    en.wikipedia.org/wiki/File:Riemann_sum_error.svg

    English: Graph showing the value of the Riemann sum approximation to (using right endpoint as rectangle height) as the number of rectangles increases. It approaches the blue line y=8/3, the actual value of the definite integral.