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Related Concept Videos

Substitutions in Multiple Integrals01:30

Substitutions in Multiple Integrals

Multiple integration is an important mathematical method used to calculate physical quantities distributed over a two-dimensional region, such as the total mass of an elliptical plate. In this process, the density function is evaluated throughout the entire region enclosed by the ellipse. The contributions from all points inside the boundary are then accumulated to determine the total mass.When integration is performed directly in rectangular coordinates, the elliptical boundary produces limits...
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Triple Integrals in Rectangular Coordinates

Triple integrals provide a method for calculating the accumulated value of a function over a three-dimensional region. Common applications include computing volume, mass, and other physical quantities that vary with position. The fundamental idea is to partition a solid region into small rectangular boxes, evaluate the function at sample points within each box, and sum the contributions. As the partitions become finer, this triple Riemann sum approaches the exact value of the triple integral.In...
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Blast Quantification Using Hopkinson Pressure Bars
09:41

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Published on: July 5, 2016

Calculation of generalized Hubbell rectangular source integral.

Jonathan Murley1, Nasser Saad

  • 1Department of Mathematics and Statistics, University of Prince Edward Island Charlottetown, Prince Edward Island, Canada.

Applied Radiation and Isotopes : Including Data, Instrumentation and Methods for Use in Agriculture, Industry and Medicine
|August 21, 2010
PubMed
Summary

A new formula simplifies calculating the generalized Hubbell radiation rectangular source integral. This study compares numerical values from the approximation formula with existing literature data.

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Area of Science:

  • Radiation physics
  • Computational physics

Background:

  • The generalized Hubbell radiation rectangular source integral is crucial in radiation transport and shielding.
  • Accurate computation of this integral is essential for reliable dosimetry and safety assessments.

Purpose of the Study:

  • To introduce a simple and efficient formula for computing the generalized Hubbell radiation rectangular source integral.
  • To validate the accuracy of the proposed approximation formula.

Main Methods:

  • Development of a novel approximation formula for the generalized Hubbell radiation rectangular source integral.
  • Numerical computation using the derived formula.
  • Comparison of results with previously published data.

Main Results:

  • A straightforward formula for the generalized Hubbell radiation rectangular source integral has been successfully derived.
  • The numerical values obtained from the approximation formula show good agreement with existing literature values.
  • Tables are provided for direct comparison, facilitating verification.

Conclusions:

  • The proposed formula offers a simplified and accurate method for calculating the generalized Hubbell radiation rectangular source integral.
  • This approximation can be valuable for radiation physics and engineering applications requiring efficient integral computation.
  • The findings contribute to improved accuracy in radiation transport calculations.