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I'm doing this integration:

I = ∫[itex]^{1}_{-1}[/itex]1/([itex]\pi[/itex]√1-x^{2})dx

I made the substitution x = cosθ, and I'm fine with performing the integral apart from changing the limits - for x = 1 I put θ = 0, but for x = -1, how do I know whether to choose θ = [itex]\pi[/itex] or θ = -[itex]\pi[/itex]? The first choice gives I = 1 but the second gives I = -1. I know arccos is defined so that 0 ≤ θ ≤ [itex]\pi[/itex], but surely choosing θ = -[itex]\pi[/itex] should work and give the same value for the integral anyway, since this is just to avoid arccos being multi valued?

Thanks

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# Changing limits of integration in subsitution

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