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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
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
by 1( ) Let ( 1
( ) for ) be a function of several variables and let t...
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- Spring '13