Math Problem Statement

Compute the flux of the vector field F = 3yi + j - 3xz k through the surface S, which is the surface y = x^2 + z^2, with x^2 + z^2 ≤ 9, oriented in the positive y-direction.

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Calculus
Surface Integrals
Flux Calculation

Formulas

Flux = ∬_S F · dS = ∬_S F · (N dA)
Normal vector for surface parameterized by y = f(x, z): N = (-∂f/∂x, 1, -∂f/∂z)

Theorems

Divergence Theorem (if used to verify)

Suitable Grade Level

Undergraduate Level (Calculus III)

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