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Miike012
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Can someone tell me where my calculations are going wrong.
I am integrating over C2: (Note Line integral over C1 and C3 are zero.)
NOTE: The vector function f(x,y,z) that I am integrating over C2 is highlighted in red in the paint doc.
The equation that I am using is: ∫[f (dot) unit tangent]ds
Equation of C2: y = 1 - x
Parameterization of C2: y = 1 - s and x = s
Vector function for C2 is: r(s) = (s,1-s)
d(r(s))/ds = (1,-1)
Unit d(r(s))/ds = (1,-1)/√2
f(x,y,z) = (y,-x) = (1-s,-s)f (dot) unit tangent = (1-s,-s) dot (1,-1)/√2 = 1/√2
Integrating line integral from 0 to √2 I get: 1/√2(s) from 0 to √2 = 1.
The answer is -1.
I am integrating over C2: (Note Line integral over C1 and C3 are zero.)
NOTE: The vector function f(x,y,z) that I am integrating over C2 is highlighted in red in the paint doc.
The equation that I am using is: ∫[f (dot) unit tangent]ds
Equation of C2: y = 1 - x
Parameterization of C2: y = 1 - s and x = s
Vector function for C2 is: r(s) = (s,1-s)
d(r(s))/ds = (1,-1)
Unit d(r(s))/ds = (1,-1)/√2
f(x,y,z) = (y,-x) = (1-s,-s)f (dot) unit tangent = (1-s,-s) dot (1,-1)/√2 = 1/√2
Integrating line integral from 0 to √2 I get: 1/√2(s) from 0 to √2 = 1.
The answer is -1.
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