{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Calc III Ch15 Notes_Part6

# Calc III Ch15 Notes_Part6 - ,W M “we/raw ma 5/0"“...

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

This is the end of the preview. Sign up to access the rest of the document.

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 C "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. ...
View Full Document

{[ snackBarMessage ]}