Chap5notes Sol

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...Chapter line and surface integrals solutions example find the work done by force f x y i xyj in moving a particle along curve which runs from to unit circle then axis see figure shows eld c is negative because impedes movement solution split into two sections that w z dr parameterise r t cost sint where xy dx dy hence xydy cos tdtdt costsintdtdt tsintdt applying beta functions solve integral m n k dxdt tdydt dt so evaluatethelineintegralr wherec istheisthearcoftheparabolax since ydx xdy tdxdt dydt evaluate straight segment we can do this question without parameterising does not change direction with on use green s theorem esinx py sinx p q e d given interior of disc such dxdy rdrd solved using polar coordinates describe ellipse anticlockwise ii directly area for calculating an variables double costsint sin tdt are calculated symmetry properties table signs below etc quadrant total ds hemisphere rst nd these terms arise relates derivatives dierentiating both sides respect giving similar...

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Posted on: 26 Jan 2023 | 4 years ago
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