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Integrate the function f(x, y, z) = 0.7(x2 + y2 + z2 ) over the unit sphere S ={(x,y, z) | x2 +y2+z2 ≤ 1} using the Monte-Carlo method in three dimensions. using a sample of M = 106 points

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Question

Integrate the function f(x, y, z) = 0.7(x² + y² + z² ) over the unit sphere S ={(x,y, z) | x² +y²+z² ≤ 1} using the Monte-Carlo method in three dimensions. using a sample of M = 106 points.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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