0-2pi-cos-x-2-

Question Number 218063 by alephnull last updated on 27/Mar/25

\int_{0}^{2 π} \cos x^{2}

Answered by Frix last updated on 28/Mar/25

The Fresnel C Integral :

C (x) := \underset{0}{\int^{x}} \cos \frac{π t^{2}}{2} d t

\Rightarrow

\underset{0}{\int^{2 π}} \cos x^{2} d x = \frac{\sqrt{2 π}}{2} {[C (\frac{\sqrt{2}}{\sqrt{π}} x)]}_{0}^{2 π} = \frac{\sqrt{2 π}}{2} C (\sqrt{8 π})

\approx . 704681810

Answered by MrGaster last updated on 29/Mar/25

Facebook Tweet Pin