Verification of the Divergence Theorem for the 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
Triple Integrals

Formulas

∇ · F = 2x + 2y + 2z
∫∫_S F · dS = ∫∫∫_V (∇ · F) dV

Theorems

Divergence Theorem

Suitable Grade Level

Grades 11-12

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