The value of s F ds for the vector field F=< r, 2ryz, z> where S is the surface of the region E that is the rectangular box-1 and S is the surface of the region bounded by z 1-r, z = 0, y = 0, y = 2 is an integer. A. What is A?
The value of s F ds for the vector field F=< r, 2ryz, z> where S is the surface of the region E that is the rectangular box-1 and S is the surface of the region bounded by z 1-r, z = 0, y = 0, y = 2 is an integer. A. What is A?
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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1. The value of the surface integral \(\iint_{S} \vec{F} \cdot d\vec{S}\) for the vector field \(\vec{F} = \langle x^2 z^3, 2xyz^3, xz^4 \rangle\) where \(S\) is the surface of the region \(E\) that is the rectangular box \(-1 \leq x \leq 1, -2 \leq y \leq 2, -3 \leq z \leq 3\) is an integer \(A\). What is \(A\)?
2. The value of the surface integral \(\iint_{S} \vec{F} \cdot d\vec{S}\) for \(\vec{F}(x, y, z) = \langle xy, (y^2 + e^{x^2}), \sin(xy) \rangle\) and \(S\) is the surface of the region bounded by \(z = 1 - x^2, z = 0, y = 0, y = 2\) is an integer \(A\). What is \(A\)?
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