Integrating Complex Exponentials

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SUMMARY

The integral of the complex exponential function e^(ix) from 0 to infinity evaluates to -1/i, despite the oscillatory nature of the function. The upper limit of the integral approaches zero, which is a critical aspect of the evaluation. This conclusion is established through a specific proof that clarifies the behavior of the integral at infinity.

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americanforest
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The integral of a complex exponential ( e^(ix) ) over x from 0 to infinity is supposedly such that the value of the definite integral at the upper limit is zero and so it's just -1/i. Why is this? It's just an oscillating function after all.
 
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Nevermind, I figured it out a way to prove it.
 

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