LineIntegral - Line Integral. Ian R. Gatland, Georgia...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Line Integral. Ian R. Gatland, Georgia Institute of Technology Physics 3122 notes, September 2, 2010 Consider a line integral, ∫ v ⋅ d , where the points on the line are specified in terms of some parameter, t, as x ( t ), y ( t ), and z( t ) . Then ˆ ˆ ˆ ∫ v ⋅ d = ∫ v ( x, y, z)⋅ ( xdx + ydy + zdz) € ȹ dx dy dz ȹ ˆ ˆ ˆ = ∫ v ( x ( t ), y ( t ), z( t ))⋅ ȹ x dt + y dt + z dt ȹ € ȹ dt dt dt Ⱥ ȹ dx dy dz ȹ ˆ ˆ ˆ = ∫ v ( x ( t ), y ( t ), z( t ))⋅ ȹ x +y + z ȹ dt ȹ dt dt dt Ⱥ where the derivatives are expressed in terms of t. € In many cases the parameter may be one of the coordinates so if t is x then ˆˆ ˆ ∫ v ⋅ d = ∫ v ( x, y ( x ), z( x ))⋅ ȹ x + y dx + z dx ȹdx ȹ Ⱥ ȹ where the derivatives are expressed in terms of x. € There are similar results when t is y and when t is z. dy dz ȹ ...
View Full Document

Ask a homework question - tutors are online