Line Integral (where the path is not single valued)

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SUMMARY

The discussion focuses on evaluating the line integral I = ∫(x+y)dx from point A (0,1) to point B (0,-1) along the semi-circle defined by x² + y² = 1 for x ≥ 0. The user correctly identifies that y can be expressed as y = √(1 - x²) and simplifies the integral to 2∫√(1 - x²)dx from 0 to 1. The solution is completed by converting to polar coordinates, where x = cos(θ) and y = sin(θ), with θ ranging from π/2 to 3π/2, and applying a negative sign due to the curve's orientation.

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I'm a bit confused as to how to solve this line integral:

Evaluate I = The integral of (x+y)dx from A (0,1) to B (0,-1) along the semi-circle
x^2 + y^2 = 1 for for x is equal to or greater than 0.

So far have have got:

if x^2 + y^2 = 1 then y= + SQRT of (1 - x^2)

which I believe boils down to : 2 times the integral of SQRT (1 - x^2) from 0 to 1.

I'm very confused how to finish this off and would appreciate any help.
 
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Use polar coordinates! Ie: x = cos(theta), y = sin(theta), theta going from pi/2 to 3pi/2. (And include an overall negative sign due to the orientation of the curve)
 

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