Prove-that-i-cos2t-isin2t-e-t-2-dt-pi-2e-

Question Number 196412 by Erico last updated on 25/Aug/23

Prove that {\int_{i}}^{+ \infty} (\cos 2 t + isin 2 t) e^{- t^{2}} dt = \frac{\sqrt{π}}{2 e}

Commented by JDamian last updated on 24/Aug/23

i s t r e a l o r c o m p l e x ?

Answered by MrGaster last updated on 16/Feb/25

\int_{0}^{+ \infty} \cos 2 t \cdot e^{- t^{2}} d t = \frac{\sqrt{π}}{2 e}

\int_{0}^{+ \infty} \sin 2 t \cdot e^{- t^{2}} d t = 0

{\int_{i}}^{+ \infty} (\cos 2 t + isin 2 t) e^{- t^{2}} dt = \frac{\sqrt{π}}{2 e}

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