HSC 2012-14 MX2 Integration Marathon (archive) (1 Viewer)

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seanieg89

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Re: MX2 Integration Marathon

Find a recursion relation for the following sequence of integrals:



where n is a non-negative integer.

Hence evaluate .
 
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Re: MX2 Integration Marathon

Are you sure the second integral works?
 

rolpsy

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Re: MX2 Integration Marathon

my solution is mathematically correct, i don't care if it's wrong :p
lol you forgot to integrate!



which gives the correct answer


here is a really difficult one:



good luck
 
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Re: MX2 Integration Marathon

that x/tanx is my mission for tonight...have currently tried trig subs, t subs, nothing...have tried int fx from 0 to a = f(a-x) 0 to a...hasn't worked.
 

Shadowless

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Re: MX2 Integration Marathon

lol you forgot to integrate!



which gives the correct answer


here is a really difficult one:



good luck
is the answer: pi/2 ?

(if the answer is right, i'll post solution when i figure out how to do all those integral signs and fractions = / )
 

rolpsy

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Re: MX2 Integration Marathon

is the answer: pi/2 ?

(if the answer is right, i'll post solution when i figure out how to do all those integral signs and fractions = / )
sorry, nope
(although interested to know your method)



i'm not particularly 'good' at 4u but correct me if i'm wrong in saying that:

tan x DOES NOT EQUAL tan( pi/4 - x )?

rather it equals tan ( pi/2 - x )


s/he's using properties of definite integrals, namely



also tan(pi/2 - x) = cot(x) :p
 

nightweaver066

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Re: MX2 Integration Marathon



i'm not particularly 'good' at 4u but correct me if i'm wrong in saying that:

tan x DOES NOT EQUAL tan( pi/4 - x )?

rather it equals tan ( pi/2 - x )


Definite integral property.



If you wish to prove, let u = a - x for LHS and proceed.
 

nightweaver066

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Re: MX2 Integration Marathon

lol you forgot to integrate!



which gives the correct answer


here is a really difficult one:



good luck






Now IIRC, that second integral is easily done by 2 applications of IBP and rearrangements.

D: i just realised its undefined at x = 0.. L'Hopital's rule?
 
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