Labware - MA35 Multivariable Calculus - Three Variable Calculus

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Path Integrals in Three-Space

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If c(t) = (x(t),y(t),z(t)) is a path in three-space and f(x,y,z) is function defined over c, then the path integral of f along c is given by c f(x,y,z) ds = ∫abf(x(t),y(t),z(t))s'(t)dt. where s'(t) = √(x'(t)2 + y'(t)2 + z'(t)2).

Demos

Exercises

  • 1. While path integrals can be carried out in two-space and three-space, they could still be considered to be part of single variable calculus. Why is this?
  • 2. Find the arc length of the curve (cos(t), sin(t), sin(2t)), 0 ≤ t ≤ 2π.