Integral from o to inf of sin(x/2)dx

[BoldKnight399]

Integral from o to inf of sin(x/2)dx

First thing I did was ditch the infinity so it became:
lim as a-->inf of integral from 0 to a of sin(x/2)dx

next I integrated it:
lim as a approaches infin of -cos(x/2) evaluated from o to a

then I plugged in:
lima->inf of -2cos(a/2)+2(cos0)

My problem is that I don't know if cos of inf diverges of converges. I know that it occelates, but what does that count as? Or, am I missing a step in here or just messed up somewhere along way? If anyone has any suggestions, I would greatly appreciate it.

 

[Mark44]

You can't take the cosine of infinity. The limit of interest, lim a --> inf -2cos(a/2) does not exist, so your original integral diverges.

 

[BoldKnight399]

ok Thank you!