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I read that integrating the ds gives the arc length along the curved manifold. So in this case, I have a unit sphere and its metric is ds^2=dθ^2+sin(θ)^2*dψ^2. So how to integrate it? What is the solution for S?

Note, it also is known as ds^2=dΩ^2

Thanks!

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# Integrating the metric in 3-D Spherical coordinates

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