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Integration help please?

qss31995.jpeg
The first part of finding I (0) was fairly straight forward, but I'm not sure how to proceed on the next part of the question where I am asked to find I (n) in terms of I (n-1). I tried integrating by parts, but that didn't seem to get me very far. Can someone point me in the right direction?

Edit: I would also like to add, even after finding the recurrence relation, I am not sure how exactly I would go about evaluating I(n) as the question did not specify that n had to be an integer value; which would mean I am required to evaluate the integral for all real n without an interger interval.
(edited 8 years ago)

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Reply 1
Avatar for TeeEm
TeeEm
19
Original post by catastrophe exam
qss31995.jpeg
The first part of finding I (0) was fairly straight forward, but I'm not sure how to proceed on the next part of the question where I am asked to find I (n) in terms of I (n-1). I tried integrating by parts, but that didn't seem to get me very far. Can someone point me in the right direction?

Edit: I would also like to add, even after finding the recurrence relation, I am not sure how exactly I would go about evaluating I(n) as the question did not specify that n had to be an integer value; which would mean I am required to evaluate the integral for all real n without an interger interval.


have you seen manipulations involving reduction formulas before?
Original post by TeeEm
have you seen manipulations involving reduction formulas before?

I'm sorry, I don't really know what you mean by a 'reduction formula'. If it is something in the further pure modules, I probably have not since I have not studied any of them yet.
Reply 3
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TeeEm
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Original post by catastrophe exam
I'm sorry, I don't really know what you mean by a 'reduction formula'. If it is something in the further pure modules, I probably have not since I have not studied any of them yet.


I am not sure on what course you are on and what is your background.
This question is Further Maths A level standard, the topic is called reduction formulas.
I do not know how to help you unless I post a solution, which is against the rules.

give me a minute I will try to find some similar questions with solutions
Original post by TeeEm
I am not sure on what course you are on and what is your background.
This question is Further Maths A level standard, the topic is called reduction formulas.
I do not know how to help you unless I post a solution, which is against the rules.
give me a minute I will try to find some similar questions with solutions

no it's fine, I've been trying this question for an hour and a half now, if it's something I'm not supposed to be able to know how to do then I'll come back to it later when I've learned the topics ^^
Please don't waste your time trying to help me out now!
Reply 5
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TeeEm
19
Original post by catastrophe exam
no it's fine, I've been trying this question for an hour and a half now, if it's something I'm not supposed to be able to know how to do then I'll come back to it later when I've learned the topics ^^
Please don't waste your time trying to help me out now!


here are 2 similar questions (ever so slightly easier)

IMG.pdf

No waste of time ...
I have written a full solution to your problem in 3 minutes and I will add it to my own resources.
Original post by TeeEm
here are 2 similar questions (ever so slightly easier)
IMG.pdf
No waste of time ...
I have written a full solution to your problem in 3 minutes and I will add it to my own resources.

By the way, just so you know, the problem was from STEP III 1995
Reply 7
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TeeEm
19
Original post by catastrophe exam
By the way, just so you know, the problem was from STEP III 1995



I am very surprised ...
either STEP III was very easy in those days or I am getting smarter in my old age ....
g8.jpg336.9KB
Original post by TeeEm
I am very surprised ...
either STEP III was very easy in those days or I am getting smarter in my old age ....

It didn't specify n was an integer though... so you had to think of all the special cases as well and when you evaluated it I don't think it is as straight forward as just applying the recurrence relation.
Reply 9
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TeeEm
19
Original post by catastrophe exam
It didn't specify n was an integer though... so you had to think of all the special cases as well and when you evaluated it I don't think it is as straight forward as just applying the recurrence relation.


well on what information you have supplied, there are some restrictions in the value of n, however the reduction formula does not assume n is an integer
Original post by TeeEm
well on what information you have supplied, there are some restrictions in the value of n, however the reduction formula does not assume n is an integer

yes, but you would have to evaluate all real values of n within an integer interval to be able to apply the reduction formula to further evaluate it for all real n.
Reply 11
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TeeEm
19
Original post by catastrophe exam
yes, but you would have to evaluate all real values of n within an integer interval to be able to apply the reduction formula to further evaluate it for all real n.


I am lost ... and this is me thinking I am getting smarter.
Reply 12
Avatar for TeeEm
TeeEm
19
this is my version of your question (adapted so I can take ownership)

EDIT
I corrected 3 typos! hope there no more ...
(edited 8 years ago)
NEW.pdf21.7KB
Original post by TeeEm
this is my version of your question (adapted so I can take ownership)


In the question you specify n≥1 n \geq 1 yet in part b) you ask for the solution when n=0 n = 0

Also, d) seems fairly trivial, but a nice question overall nonetheless!
Reply 14
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TeeEm
19
Original post by Duskstar
In the question you specify n≥1 n \geq 1 yet in part b) you ask for the solution when n=0 n = 0

Also, d) seems fairly trivial, but a nice question overall nonetheless!


I could be wrong but have a little think ...

somebody else was asking the same thing in another question no so long ago.
Original post by TeeEm
I could be wrong but have a little think ...

somebody else was asking the same thing in another question no so long ago.


I wasn't saying it's incorrect, just that the way you wrote the question implies the integration isn't valid for n=0 ?
Reply 16
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TeeEm
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Original post by Duskstar
I wasn't saying it's incorrect, just that the way you wrote the question implies the integration isn't valid for n=0 ?


I see...
you are correct

this should be in the next expression ... only a fast draft with loads of copy and paste.
Did you manage part b/c
Original post by TeeEm
I see...
you are correct

this should be in the next expression ... only a fast draft with loads of copy and paste.
Did you manage part b/c


I can do b, but not c - I'm not aware of having covered the maths for it (that is a matrix in the answer, right?), and you mentioned this is FP2 territory, which would explain it.
Reply 18
Avatar for TeeEm
TeeEm
19
Original post by Duskstar
I can do b, but not c - I'm not aware of having covered the maths for it (that is a matrix in the answer, right?), and you mentioned this is FP2 territory, which would explain it.


no matrix

binomial coefficient AS but very hard to manipulate
Original post by TeeEm
no matrix

binomial coefficient AS but very hard to manipulate


Oh okay, I'll have to have a sit down and try and do that one :smile:

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