Definite integrals, evaluate the question

Evaluate:
http://s23.postimage.org/9owf436xz/Untitled.jpg
answer given is ln(√3) <-- I dont get this answer
thanks in advance

Well, let's step through the problem. First let's you have to integrate cotx. To do this, we need a little u substitution.

recall that cotx = cosx/sinx
also recall that derivative(sinx) = cosx
So we can say u = sinx, du = cosx

And so we want integral(u/du) which is:

ln(u) + C

substitute back in for u:

ln(sinx) + C

Now evaluate it from pi/3 to pi/6

ln(sin(pi/3)) - ln(sin(pi/6)) = ln(sqrt(3)/2) - ln(1/2)

Recall that lnx - lny = ln(x/y)

since sqrt(3)/2 divided by 1/2 = sqrt(3),

the answer is ln(sqrt(3))