integration (1 Viewer)

[haboozin]

find integral of

cosec x dx

using sub t= tan x/2


cheers

 

[Dumsum]

Let I = ∫cosecx.dx

I = ∫1/sinx . dx


Let t = tan(x/2)
dt/dx = 1/2 . sec^2 (x/2)
dx = 2/[sec^2 (x/2)] . dt = 2/[1+tan^2 (x/2)] . dt = 2/(1+t^2) . dt

sinx = 2t/(1+t^2) (using 't' results)

Therefore,

I = ∫(1+t^2)/2t . 2/(1+t^2) . dt
= ∫1/t . dt
= lnt + c
= ln[tan(x/2)] + c

 

[who_loves_maths]

if you know a bit about mathematical symmetry, then you can probably guess first that:

I[cosec x dx] = -ln(cosecx + cot x) + c ;

this follows from I[sec x dx] = ln(secx + tan x) + c

 

[FinalFantasy]

hey 'who_loves_maths' u look like another high lvl maths person, newly arrived at this site! r u year of 05?

 

[who_loves_maths]

hi FinalFantasy, yeah i am a 2005er. lol, i've been coming to boredofstudies for quite awhile now, just never saw that "forum" tab on the left hand side i guess, lol.