mechanics plz help. (1 Viewer)

[FinalFantasy]

yea dats a damn nice move...
i think i probably won't be able to come up with that during an exam

i better go now...

and plz.. no more saying things about me!!
i am really not as good as u think and i probably won't even get a 90 in mx2 since i stuffed da half yearlies pretty bad

ttyl!!

 

[maths > english]

lol, theres no way youll get below 90 in mx2 final fantasy

u only need to beat 75% of 4u students to get 91 and there are alot of idiots doing 4u

people at my school last year couldnt even do the integration questions at the start of the 4u exam

 

[who_loves_maths]

okay, ttyl FinalF.

and in case you might read this thread again some other time:

i had a thought about that question just then and it's pretty easy to work out even without the first part of the question that KFunk provided that leads you into doing the second part - in fact, you don't really need a "lead-in", it should automatically become part of your working out if you try to just do the integral on its own, this is what i just did:

Int[ln(1+tanx)dx] between {0, and pi/4):

using special properties of definite integrals - original integral = Int[ln(1+tan(pi/4 -x))dx] between {0, and pi/4} ;
now, tan(pi/4 -x) = (tan(pi/4) - tanx)/(1 + tan(pi/4)*tan(x)) = (1-tanx)/(1+tanx) = (cosx -sinx)/(cosx +sinx) ;
hence, Int[ln(1+tan(pi/4 -x))dx] = Int[ln(1 +(cosx -sinx)/(cosx +sinx))dx] = Int[2cosx/(cosx +sinx)dx] ;
now, the original integral: Int[ln(1+tanx)dx] = Int[ln((cosx+sinx)/cosx)dx] ;

hence, 2I = Int[2cosx/(cosx +sinx)dx] + Int[ln((cosx+sinx)/cosx)dx] = Int[ln(2) dx] between {0, and pi/4} ;
ie. 2I = ln(2)*(pi/4) -----> I = ln(2)*(pi/8)


see? the whole thing by itself without the need of a "lead-in" is not long at all

 

[FinalFantasy]

int. f(x) from 0 to a=int. f(a-x) from 0 to a
that thing isn't supposed to be in the 4u syllabus, u gota derive it first i think

 

[who_loves_maths]

Originally Posted by FinalFantasy
int. f(x) from 0 to a=int. f(a-x) from 0 to a
that thing isn't supposed to be in the 4u syllabus, u gota derive it first i think..

are you sure it's not part of the syllabus? cause every class in our school learnt it... it's part of the Patel and Excel books, and it was part of our exams once too.

plus, the derivation is quite simple, just let X=a-x , and go from there...

 

[shafqat]

It's in the syllabus, but you can't assume the result. They'll ask you to prove it before giving a question that uses the result.

 

[haboozin]

int. f(x) from 0 to a=int. f(a-x) from 0 to a
that thing isn't supposed to be in the 4u syllabus, u gota derive it first i think

yea thats definatly in the syllabus there is a whole chapter on it aswell..

last chapter in integration in cambridge.

 

[FinalFantasy]

yea i saw it in da cambridge book.. but i remember someone saying it's not in da syllabus.. o well i was wrong