Math Problem Statement
evaluate the integral ∫∫∫v dzdydx over the sphere x^2 +y^2 +z^2 =a^2
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Spherical Coordinates
Triple Integrals
Formulas
Spherical coordinates: x = r sin(θ) cos(φ), y = r sin(θ) sin(φ), z = r cos(θ)
Volume element in spherical coordinates: dV = r^2 sin(θ) dr dθ dφ
Theorems
Triple Integration in Spherical Coordinates
Volume of a Sphere
Suitable Grade Level
Undergraduate Calculus
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