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?