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Line integral question
The question
For the vector field F  = (x^2 + y^2 + z^2))
i - zj + (y + 1)k calculate 
where the path C from (0, 0, -1) to (0, 0, 1) is the circle 
in the plane x = 0, the direction of motion being anti-clockwise when viewed from the positive x-axis.
My attempt
Let z = sin(t), y = cos(t)
C(t) = (0, cos(t), sin(t))
C'(t) = (0, -sin(t), cos(t))
F(C(t)) =  + sin^2(t)))
i - )
j +  + 1))
k
= i - sin(t)j + (cos(t) + 1)k
(1, -sin(t), cos(t) + 1).(0, -sin(t), cos(t))
= 1 + cos(t)
 \ dt})
= 2 + 2sin(1)
However the solution is 
.
Where have I gone wrong? Thanks.
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With the parametric equations you give, t goes from 0 to 
(around the full circle), not -1 to 1.
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Ahh, I see. So it wouldn't be 
to 
? Or it doesn't matter?
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Hmm, now I'm getting , which is also wrong. :/
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I can't see where I'm going wrong, is the rest of the working correct?
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the limits of your integration should be from 
to 
(you are only tracing out a semi-circle in the yz-plane if C goes from (0,0,-1) to (0,0,1) counter-clockwise along the circle).
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Thank you. I was a bit confused when HallsofIvy said 0 to 2pi.
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Sorry, I misread the problem, thinking you were integrating around the entire circle. I wondered where you got -1 and 1 from!
