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

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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’...
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