Verifying the Divergence Theorem for Vector Field F=x^2 i+y^2 j+z^2 k

Math Problem Statement

To verify the Divergence Theorem for the vector field 𝐹=𝑥2 𝑖+𝑦2 𝑗+𝑧2 𝑘 over the closed surface 𝑆 in the first octant bounded by the coordinate planes and the plane 𝑥+𝑦+𝑧=𝑎

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Calculus
Divergence Theorem
Triple Integrals

Formulas

∇·F = ∂P/∂x + ∂Q/∂y + ∂R/∂z
∭_V (∇·F) dV
∬_S F·dS

Theorems

Divergence Theorem

Suitable Grade Level

Grades 11-12

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