Here s where c is given by c sin 0 is

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: for 0 ≤ ≤ 2π . Here, S , where C is given by + C = ( − sin ), = > 0 is some constant. First, = (1 − cos ) = sin and hence 2π (2 − ) + (1 + cos ) (1 − cos ) + ( − sin ) sin = C 2π 2π 1 − cos2 + sin − sin2 2 = 2 − cos 0 3 = 0 2π + 0 cos = −2π 2 :) 0 Questions on logical thinking E Prove that the value of a line integral of a function does not depend on the parametrization of the curve. Specifically, assume that a curve C is given by a parametric equation x = x( ) and let = ( ) be some monotonic (increasing or decreasing) function. Prove that the value of the integral C is the same whether we take or as a parameter. S by 1( ) Let ( 1 ( ) for ) be a function of several variables and let t...
View Full Document

Ask a homework question - tutors are online