Integral of sin(a x) from 0 to ∞

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SUMMARY

The integral of sin(ax) from 0 to infinity is indeterminate, as established in the discussion. The behavior of the integral from 0 to x is sinusoidal, leading to non-convergence as x approaches infinity. Therefore, it does not yield a specific value in the context of generalized functions.

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In terms of generalized functions, the integral from zero to infinity sin (a x) dx is equal to what?
 
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Hi fab:

The integral value is indeterminant. The integral from 0 to x is sinusoidal, so the integal value from 0 to inf does not converge to a specific value as x goes to inf.

Regards,
Buzz
 
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