What are the limits for the integral of sin(x) * sin(x^2)?

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LordVader88
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I've never cracked this 1 yet, and I don't remember if it's domain was [0,1] or [0,∞), pretty sure it was 1 of the 2, and not anything with -∞ or ∏/2 for example

∫[sinx * sin(x^2)]dx
 
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sin(x)* sin(x^2)=[sin((x-1/2)^2)-sin((x+1/2)^2)]sin(1/4)/2+[cos((x-1/2)^2)-cos((x+1/2)^2)]cos(1/4)/2

Your integral is then easily expressed in terms ofFresnel integrals. As far as what limits make the answer tidy, probably none.