Calculate ff f(x, y, z) dS For Part of the surface x = z³, where 0 < x, y ≤ 8 - 1²2 ; f(x, y, z) = = X s f(x, y, z) dS = ¯
Calculate ff f(x, y, z) dS For Part of the surface x = z³, where 0 < x, y ≤ 8 - 1²2 ; f(x, y, z) = = X s f(x, y, z) dS = ¯
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Calculate the surface integral \(\iint_S f(x, y, z) \, dS\) for the part of the surface where \(x = z^3\), and the region is defined by \(0 \leq x, y \leq 8^{-\frac{3}{2}}\).
Given:
\[ f(x, y, z) = x \]
You need to evaluate:
\[
\iint_S f(x, y, z) \, dS = \boxed{}
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Transcribed Image Text:Calculate the surface integral \(\iint_S f(x, y, z) \, dS\) for the part of the surface where \(x = z^3\), and the region is defined by \(0 \leq x, y \leq 8^{-\frac{3}{2}}\).
Given:
\[ f(x, y, z) = x \]
You need to evaluate:
\[
\iint_S f(x, y, z) \, dS = \boxed{}
\]
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