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Compute the total mass of a wire bent in a quarter circle with parametric equations: a = 4 cost, y = 4 sint, 0≤t≤ and density function p(x, y) = x² + y².

Compute the total mass of a wire bent in a quarter circle with parametric equations: a = 4 cost, y = 4 sint, 0≤t≤ and density function p(x, y) = x² + y².

Advanced Engineering Mathematics
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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Compute the total mass of a wire bent in a quarter circle with parametric equations: a = 4 cost, y = 4 sint, 0≤t≤ and density function p(x, y) = x² + y².
Transcribed Image Text:Compute the total mass of a wire bent in a quarter circle with parametric equations: a = 4 cost, y = 4 sint, 0≤t≤ and density function p(x, y) = x² + y².
Consider the vector field F = (x² + y², 5xy). Compute the line integrals F. dr and f, F-dr, where c₁ (t) = (t, t²) and c₂(t) = (t, t) for 0 ≤ t ≤ 1. Can you decide from your answers whether or not F is a gradient vector field? Why or why not? Je, F-dr = Je, F. dr = Is F conservative? (yes/no)
Transcribed Image Text:Consider the vector field F = (x² + y², 5xy). Compute the line integrals F. dr and f, F-dr, where c₁ (t) = (t, t²) and c₂(t) = (t, t) for 0 ≤ t ≤ 1. Can you decide from your answers whether or not F is a gradient vector field? Why or why not? Je, F-dr = Je, F. dr = Is F conservative? (yes/no)
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