I need help with an integration problem

[doniarahhal]

Does any one know how can you solve this equation
∫_0^(π/2)▒cot⁡〖θd θ〗
the integral from 0 to π/2 of cotθ dθ.
any help would be appreciated
thank you

 

[HallsofIvy]

\(\displaystyle \int_0^{\pi/2} \cot(\theta)d\theta\).

I recall that \(\displaystyle \cot(\theta)= \frac{\cos(\theta)}{\sin(\theta)}\)
so that the integral can be written \(\displaystyle \int_0^{\pi/2} \frac{\cos(\theta)}{\sin(\theta)}d\theta\).

I also recall that the derivative of \(\displaystyle \sin(\theta)\) is \(\displaystyle \cos(\theta)\) and that makes me think of the substitution \(\displaystyle u= \sin(\theta)\).

What do you get when you make that substitution?

(Oh dear, oh dear, oh dear- there is a problem at \(\displaystyle \theta= 0\)!)

 

[Dr.Peterson]

Does any one know how can you solve this equation
∫_0^(π/2)▒cot⁡〖θd θ〗
the integral from 0 to π/2 of cotθ dθ.
any help would be appreciated
thank you

So, have you learned anything about improper integrals?