Does the Integral \(\int_0^\infty \sin(x) \, dx\) Have a Definite Value?

jollage · Oct 3, 2013

Hi

Does this integral have a definite value [itex]\int^{\infty}_0 sin(x)dx[/itex]?

Jo

arildno · Oct 3, 2013

What is the requirement for an improper integral of this type to exist?

jollage · Oct 3, 2013

arildno said:

What is the requirement for an improper integral of this type to exist?

Thanks. So you imply it's not a well-defined integral. Actually the original integral is [itex]\int^{\infty}_0 sin(x) e^x dx[/itex]. This original integral comes from a step during my derivation of the solution to the IBVP of Burger's equation. This original one seems more absurd, isn't it?

Jo

arildno · Oct 3, 2013

Sure.
Most likely, you have missed a minus sign in the exponent, in which case the integral will exist.

jollage · Oct 3, 2013

arildno said:

Sure.
Most likely, you have missed a minus sign in the exponent, in which case the integral will exist.

I see your point. Thanks.

Jo

Does the Integral \(\int_0^\infty \sin(x) \, dx\) Have a Definite Value?

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Does the Integral \(\int_0^\infty \sin(x) \, dx\) Have a Definite Value?

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