The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

FP3 reduction question

In=(limits between 0 and 1) ∫1/(x²+a²)n dx where a and n are constants and a≠0
a) Show that for n≠0, 2na²I[n+1]=(2n-1)In+(1+a²)-n

No idea how to get started although maybe using a substitution somewhere?
(edited 9 years ago)
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by bobbricks
In=∫1/(x²+a²)n dx where a and n are constants and a≠0
a) Show that for n≠0, 2na²I[n+1]=(2n-1)In+(1+a²)-n

No idea how to get started although maybe using a substitution somewhere?


write as 1 . (x2 + a2)-n and use parts

it is very quick
Reply 2
Avatar for bobbricks
bobbricks
OP
19
Okay, cheers :biggrin:
The next part b) :
Use this integral to evaluate a=2 and n=5/2

Stuck on this now :frown:
Reply 3
Avatar for TeeEm
TeeEm
19
Original post by bobbricks
Okay, cheers :biggrin:
The next part b) :
Use this integral to evaluate a=2 and n=5/2

Stuck on this now :frown:

Do you mean?
"Use this reduction formula with a=2 and n=5/2 ...

surely you cannot be stuck at this ... this is just number-crunching
Reply 4
Avatar for TeeEm
TeeEm
19
Original post by bobbricks
Okay, cheers :biggrin:
The next part b) :
Use this integral to evaluate a=2 and n=5/2

Stuck on this now :frown:



Original post by TeeEm
Do you mean?
"Use this reduction formula with a=2 and n=5/2 ...

surely you cannot be stuck at this ... this is just number-crunching


you may some fully solved examples useful in this link

http://madasmaths.com/archive/maths_booklets/further_topics/integration/reduction_formulas.pdf
Reply 5
Avatar for bobbricks
bobbricks
OP
19
Original post by TeeEm
Do you mean?
"Use this reduction formula with a=2 and n=5/2 ...

surely you cannot be stuck at this ... this is just number-crunching


I'd sub in those values but I can't see how this simplifies it because of the "n+1" which doesn't 'reduce' the integrals
Reply 6
Avatar for TeeEm
TeeEm
19
Original post by bobbricks
I'd sub in those values but I can't see how this simplifies it because of the "n+1" which doesn't 'reduce' the integrals


look at some applications in the link I gave you
Reply 7
Avatar for dandroff
dandroff
2
Original post by bobbricks
I'd sub in those values but I can't see how this simplifies it because of the "n+1" which doesn't 'reduce' the integrals


how do i see the answers on that link ?
Reply 8
Avatar for TeeEm
TeeEm
19
Original post by dandroff
how do i see the answers on that link ?


download PDF, enlarge on a computer screen
NOT for phones
Reply 9
Avatar for dandroff
dandroff
2
Original post by TeeEm
download PDF, enlarge on a computer screen
NOT for phones

how do i view it on PDF?? sorry
Reply 10
Avatar for TeeEm
TeeEm
19
Original post by dandroff
how do i view it on PDF?? sorry


download the file from the site
Original post by TeeEm
download the file from the site


im so sorry for asking again but how do i download the file from the site?? it doesnt let me click anything on it

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you