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发帖数: 1437 | 1
Fresnel Integral
Integral[sin(x^2), {x, 0, Inf} ] = sqrt(pi/2)/2
Gven sin((-x)^2) = sin(x^2), so from -Inf to Inf,
it is sqrt(pi/2)
Same to cos(x^2), so
Result is
sqrt(pi/2) + i*sqrt(pi/2)
The way to get Fresnel Integral is build
Int(sin(t)*exp(-ut)/sqrt(t)), where u is parameter,
and exchange 积分顺序, then you will get it. |
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