Evaluate the integral: (Question will be posted ASAP)

Question

anonymous · Answer

$$\int\limits_{0}^{\frac{ \pi }{ 2 }} \tan \frac{ x }{ 2 }dx$$

hartnn · Answer

substitute t=x/2
then there is standard formula for integral of tan t

zzr0ck3r · Answer

ln |sec x| + C  
is the integral for tan(x)

anonymous · Answer

I am not typing..

zzr0ck3r · Answer

lol what @waterineyes ?

anonymous · Answer

$$\int\limits_{0}^{\frac{ \pi }{ 2 }} tant  dx?$$

hartnn · Answer

u must change the limits also and substitute for dx also

anonymous · Answer

@zzr0ck3r really??

hartnn · Answer

dt=dx/2

zzr0ck3r · Answer

I thought, maybe not...

hartnn · Answer

when x=0,t=0
when x=pi/2, t=pi/4

zzr0ck3r · Answer

-2ln(cos(x/2)) then do the bounds.

hartnn · Answer

$$2\int\limits_{0}^{\pi/4} \tan t dt$$

hartnn · Answer

got this?

anonymous · Answer

yep :)

anonymous · Answer

and then?

hartnn · Answer

now integral of tan t is -ln|cos t| or ln|sec t|
put the limits from 0 to pi/4

hartnn · Answer

and don't forget 2

anonymous · Answer

how can the integral of tan t be -ln|cost| or ln|sect| ?

hartnn · Answer

ok if u want proof of integral of tan t
write tan t as sin t/cos t
whats the derivative of cos t ??

anonymous · Answer

-sin t?

anonymous · Answer

@zzr0ck3r I was seeing continuously "waterineyes is typing a reply"..
And actually I was not typing..

So, I mentioned that..

Ha ha ha..

anonymous · Answer

lol @waterineyes >.>

anonymous · Answer

Ha ha ha ha..

anonymous · Answer

Now concentrate on your question...

anonymous · Answer

well, I'm waiting for hartnn's reply =3=

hartnn · Answer

right,its - sin t
so u write 
tan x as
-(- sin t / cos t)
now tell me do u see the derivative of denominator in numerator??

hartnn · Answer

*tan t

anonymous · Answer

Wow hartnn is replying to two questions at the same time..

I am wondering..

hartnn · Answer

ok,i stopped other...

anonymous · Answer

I see it... but I still don't get your point ^.^;

hartnn · Answer

ok,now u will
$$\int\limits_{}^{} \frac{f \prime (x)}{f(x)}dx=\ln|f(x)|+c$$
this is standard relation,i have used this.

hartnn · Answer

this can be applied when u see the derivative of denominator in numerator

anonymous · Answer

ohhhhhhhhhhhhhhhh

anonymous · Answer

wait....I'm still ingesting....

anonymous · Answer

is the answer $$-2\ln \frac{ \sqrt{2} }{ 2 } ?$$

anonymous · Answer

oh, it can be simplified to ln2

anonymous · Answer

yaaaay

anonymous · Answer

thanks again Hartnn :)

hartnn · Answer

yup thats correct :)
welcome

zzr0ck3r · Answer

lol @waterineyes