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Chapter 14: Q. 15 (page 1119)

Use what you know about average value from previous sections to propose a formula for the average value of a multivariate function f(x, y, z) on a smooth surface S.

Short Answer

Expert verified

Hence,theaveragevalueofamultivariatefunctionf(x,y,z)onasmoothsurfaceSis,favg(S)=鈭�S鈥�f(x,y,z)dS鈭�S鈥�1dS

Step by step solution

01

Step 1. Given

The given function is f(x, y, z) .

02

Step 2. Finding the average value of multivariable function

Surfaceintegralsofmultivariatefunctionsf(x,y,z)is,鈭�f(x,y,z)dS.ThesurfaceareaofthesmoothsurfaceSis,鈭�S1dSHence,theaveragevalueofamultivariatefunctionf(x,y,z)onasmoothsurfaceSis,favg(S)=鈭�S鈥�f(x,y,z)dS鈭�S鈥�1dS

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