Unformatted text preview: ,W M “we/raw ma 5/0"“ 0 Line Integrals. Line gzgralsD are essentially integrating a function ove1 the length of a curve. ‘ ‘
(WV! .ZWVZI 0&5 ' . Iﬂ/fifMﬁr $910M? fez/’05 Illustration. I like to think of them as the integrand being a density function, so the line
integral will give the entire mg i g of a “string or wire”. If f(x, y, 2) represents the density of a wire, and As]. represents the length
. of a small segment of wire, then the mass of that segment would be
45" Z £661ZZ) 15—50 . Adding up an inﬁnite number of inﬁnitely
small segments would give //[/(/)//W Z) 45
"l . . . ,1 .
Formally, a line integral IS deﬁned as . ‘
m M - M g M“ We V 'y IL/Mx/I—JO Practically, we use a helpful theoremzc 2- D: X / 71/va D/ Mayra) W) (m; 0L6
/ WWW) “WW 4 1, NOTE: Some textbooks use different notation: / /(X:)/ a» 2(9) //f 7071 Ex: Evaluate L (2 + x 2y)ds where C is the upper half of the unit circle. ...
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- Winter '08