lect14_2

lect14_2 - Line Integrals - (14.2) Let C be a curve in R 2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Line Integrals - (14.2) Let C be a curve in R 2 or in R 3 . The curve C is said to be oriented if there is a direction to it. For example, C : r ! ! t " "# 2cos t , 2sin t $ ,0 ! t ! ! 2 . The curve C is oriented since it goes from the point 2, 0 to 0, 2 counterclockwise as t increases from 0 to ! 2 . Line Integrals Let C be an oriented curve which is represented by parametric representations: r ! ! t " "# x ! t " , y ! t " , z ! t " $ , a ! t ! b where functions x ! t " , y ! t " and z ! t " have continuous first derivatives. Let f ! x , y , z " be continuous in a region D which contains the curve C . 1. The line integral of f ! x , y , z " with respect to arc length along the oriented curve C : " C f ! x , y , z " ds " " a b f ! x ! t " , y ! t " , z ! t "" ! x % ! t "" 2 & ! y % ! t 2 & ! z % ! t 2 dt " " a b f ! r ! ! t || r ! ! t " || dt Similarly, we have, " C f ! x , y " ds " " a b f ! x ! t " , y ! t x % ! t 2 & ! y % ! t 2 dt 2. The line integral of f ! x , y , z " with respect to x along the oriented curve C : " C f ! x , y , z " dx " " a b f ! x ! t " , y ! t " , z ! t x % ! t " dt Similarly, the line integral of f ! x , y , z " with respect to x along the oriented curve C : " C f ! x , y , z " dy " " a b f ! x ! t " , y ! t " , z ! t y % ! t " dt 3. The line integral of F !
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

lect14_2 - Line Integrals - (14.2) Let C be a curve in R 2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online