MedVision ad

Integration by Substitution help needed please (1 Viewer)

blackops23

Member
Joined
Dec 15, 2010
Messages
428
Gender
Male
HSC
2011
Hi guys, I was doing an integration question:

Q. integrate 1/{(x)[root(1+x^2)]} limits: 1(<)x(<)infinity

where i used the substitution x=tanA

and ended up with having to integrate cosecA.But the problem I had was changing the integral limits.

I mean for x=1, obviously A=pi/4. But what on earth do you do for x=infinity? I mean inverse tan (infinity) =???????

Help with this inverse tan infinity thing would greatly be appreciated.

Thankyou very much.
 

kr73114

Member
Joined
Aug 6, 2009
Messages
373
Gender
Male
HSC
2011
wouln't the other limit be pi/2 for x=infinity. soz im not sure
 

stampede

doin it tuff
Joined
Nov 22, 2009
Messages
483
Gender
Undisclosed
HSC
2009
because as x approaches infinity tan inverse x approaches pi/2

 

blackops23

Member
Joined
Dec 15, 2010
Messages
428
Gender
Male
HSC
2011
OH SHIT lol, kept thinking of the graph of tan(x) not inverse tan(x).... :((

Thanks guys for the help

FOLLOW UP QUESTION:

How do you integrate csc x?
 
Last edited:

stampede

doin it tuff
Joined
Nov 22, 2009
Messages
483
Gender
Undisclosed
HSC
2009
cosec x is (sinx)^-1
then do it via t method or someshit
 

funnytomato

Active Member
Joined
Jan 21, 2011
Messages
847
Gender
Male
HSC
2010
OH SHIT lol, kept thinking of the graph of tan(x) not inverse tan(x).... :((

Thanks guys for the help

FOLLOW UP QUESTION:

How do you integrate csc x?
there are many ways to integrate cosec x
I would just multiply it by (cosec x +cot x )/(cosec x +cot x)

then factorise -1 at the front, then it becomes a log
 
Last edited:

funnytomato

Active Member
Joined
Jan 21, 2011
Messages
847
Gender
Male
HSC
2010
the answer would be -ln (cot x + cosec x) if i didn't make a mistake
 

blackops23

Member
Joined
Dec 15, 2010
Messages
428
Gender
Male
HSC
2011
the answer would be -ln (cot x + cosec x) if i didn't make a mistake
ok so say that is what happens when you have integrated cscx, with limiters pi/4(<)x(<)pi/2. cot(pi/2) is undefined -- so how do i do this question?

Appreciate the help :)
 

funnytomato

Active Member
Joined
Jan 21, 2011
Messages
847
Gender
Male
HSC
2010
ok so say that is what happens when you have integrated cscx, with limiters pi/4(<)x(<)pi/2. cot(pi/2) is undefined -- so how do i do this question?

Appreciate the help :)
cot(pi/2) is undefined???
isn't it 0?
 

blackops23

Member
Joined
Dec 15, 2010
Messages
428
Gender
Male
HSC
2011
cot(pi/2) is undefined???
isn't it 0?
crap, it is... I thought tan pi/2 was undefined, so cot pi/2 was also undefined...?? like on my calculator 1/tan(pi/2) is undefined, yet the graph of cot x says otherwise?

What exactly is going on?
 
Last edited:

stampede

doin it tuff
Joined
Nov 22, 2009
Messages
483
Gender
Undisclosed
HSC
2009
crap, it is... I thought tan pi/2 was undefined, so cot pi/2 was also undefined...?? like on my calculator 1/tan(pi/2) is undefined, yet the graph of cot x says otherwise? What exactly is going on?
tan pi/2 is infinity basically or approaches it
thus 1/tan(pi/2) is like saying 1/10000000000000000000000000 which is pretty much going towards 0
do u understand
 

blackops23

Member
Joined
Dec 15, 2010
Messages
428
Gender
Male
HSC
2011
tan pi/2 is infinity basically or approaches it
thus 1/tan(pi/2) is like saying 1/10000000000000000000000000 which is pretty much going towards 0
do u understand
but isnt that involving limits and such? I mean, the exact value of tan pi/2 is undefined... or is it infinity??
 
Last edited:

Trebla

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,385
Gender
Male
HSC
2006
The strict definition of cot x is NOT 1/tan x. The definition of cot x is in fact (cos x)/(sin x) and it is only equal to 1/tan x if tan x is defined.
 

blackops23

Member
Joined
Dec 15, 2010
Messages
428
Gender
Male
HSC
2011
The strict definition of cot x is NOT 1/tan x. The definition of cot x is in fact (cos x)/(sin x) and it is only equal to 1/tan x if tan x is defined.
aahh i see thanks trebla, and yeah i did get ln(1+root2)
 

Drongoski

Well-Known Member
Joined
Feb 22, 2009
Messages
4,255
Gender
Male
HSC
N/A
the answer would be -ln (cot x + cosec x) if i didn't make a mistake
Answer is correct (don't forget the arbitrary constant) - easily verified by differentiating wrt x your answer - should give back cosec x
 

funnytomato

Active Member
Joined
Jan 21, 2011
Messages
847
Gender
Male
HSC
2010
Answer is correct (don't forget the arbitrary constant) - easily verified by differentiating wrt x your answer - should give back cosec x
lol, this reminds me of the joke about the integral of x^2 in some Jeff Geha study guide
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top