Tutorial08-sol(1)

# Then 2 x 1 c 1 and we need to check that this

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: he curve C be given ≤ ≤ . Then 2 (x) = ( ) 1 C =1 and we need to check that this expression doesn’t change if we substitute = ( ). Assume that = ( ) is a bijective continuously diﬀerentiable function from [α β] to [. Then = · = and we need to consider two diﬀerent situations — 3 > 0 and < 0. > 0, then First, if 2 ( ) 1 2 β = ( ) 1 α =1 =1 =1 Similarly, if < 0, then 2 ( 1 ) 2 α ( = 1 β =1 − ) =1 =−1 Both formulae in are the same as the original one in . :) E Prove that the value of a line integral of a vector ﬁeld does not depend on the parametrization. S Consider a vector ﬁeld in R with components P1 be given by 1 ( ) ( ) for ≤ ≤ . Then P P and let the curve C P = C =1 =1 and we need to check that this expression doesn’...
View Full Document

## This document was uploaded on 02/10/2014.

Ask a homework question - tutors are online