Help with reduction formula

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February 2nd 2008, 02:03 PM
player07

Help with reduction formula

Hi, i want to have a reduction formula for this problem i hope that you can help me with this :)
J[k] = int((x^2-121)^k, x = 0 .. 11)

thanks in advance:)
February 2nd 2008, 04:23 PM
mr fantastic

Quote:

Originally Posted by player07

Hi, i want to have a reduction formula for this problem i hope that you can help me with this :)
J[k] = int((x^2-121)^k, x = 0 .. 11)

thanks in advance:)

Assuming you're familiar with the hyperbolic functions sinh and cosh, I think the simplest approach (and I leave myself wide open to an *ahem* from someone like Krizalid) is to first make the substitution $x = 11 \cosh^2 t$ .

This will lead to $J_k = 11^{2k + 1} \int \sinh^{2k+1} t \, dt$ which can be done using a well known reduction formula (that you might find easier to derive):

$\int \sinh^m t \, dt = \frac{\sinh^{m-1}t \, \, \cosh t}{m} - \frac{m-1}{m} \int \sinh^{m-2} t \, dt$ .

Then just sub back $\frac{x}{11} = \cosh t$ ....
February 3rd 2008, 02:33 AM
player07

Hi mr fantastic, maybe you have missunderstand what i have written
i will rewrite the question
the reduction formula for this :

http://213.89.80.30:8080/math%20problem.jpg

can you look again to the question please.
February 3rd 2008, 07:22 AM
bobak

He really didnt misunderstnad you.
You have misunderstood him!
February 3rd 2008, 10:07 AM
player07

thank you for you help :)