Can Jordan's Lemma be applied to clockwise contours?

[WWCY]

Homework Statement

My notes state the Lemma as shown above. I believe one of the underlying conditions is that the arc we integrate over must be +ve oriented (anti-clockwise) in the Upper and Lower half of the Complex Plane. However my notes doesn't mention whether or not the result holds when we integrate over a -ve oriented arc.

My question is, does it hold for clockwise contours? If so (or not), why not?

Assistance is greatly appreciated!

2. Homework Equations

The Attempt at a Solution

 

[FactChecker]

When the integration path is reversed, the sign of the integral is reversed. Since the conclusion of Jordan's lemma is that the integral goes to 0, reversing the integration path just makes the integral go to -0 = 0.

 

[WWCY]

When the integration path is reversed, the sign of the integral is reversed. Since the conclusion of Jordan's lemma is that the integral goes to 0, reversing the integration path just makes the integral go to -0 = 0.

Is this to say that I can use Jordan's Lemma in a clockwise contour?

Thank you for your response.