What Happens to the Integral of Cosine as k Approaches Infinity?

[maverick_76]

okay so I have this integral:

2∫cos(kx)dk

The bounds are from zero to infinity, this doesn't converge but is there any other way to describe this?

 

[Mark44]

okay so I have this integral:

2∫cos(kx)dk

The bounds are from zero to infinity, this doesn't converge but is there any other way to describe this?

Like this? $2\int_0^{\infty}\cos(kx) dk$
Because the upper limit of integration is ∞, this is an improper integral. You can't just "plug in" ∞ when you evaluate the antiderivative -- you need to use limits to evaluate it.

 

[maverick_76]

okay so the limit would be lim_k->∞ sin(kx)
xHow would I go about evaluating it? Is there a substitution trick?

 

[Mark44]

okay so the limit would be lim_k->∞ sin(kx)
xHow would I go about evaluating it? Is there a substitution trick?

The limit doesn't exist because sin(kx) oscillates endlessly.

 

[maverick_76]

okay gotcha. Thanks!