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

[jollage]

Hi

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

Jo

 

[arildno]

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

 

[jollage]

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 $\int^{\infty}_0 sin(x) e^x dx$. 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]

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

 

[jollage]

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