I want to evaluate the following 2 integrals:

I think this is correct.

But is more difficult:

Using integration by parts I let:

(double angle formula used)

Sine term vanishes at both limits while cosine term as 1 at both limits:

This is obviously wrong since the units don't add up. How can there be and at the same time? They both have the dimension of meters. My answer should be in meters squared. I spend hours checking and still can't find my mistake.

I plug the equation into a graphic calculator, I think the answer should be: