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:)

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- Feb 2nd 2008, 02:03 PMplayer07Help 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:) - Feb 2nd 2008, 04:23 PMmr fantastic
*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 $\displaystyle x = 11 \cosh^2 t$.

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

$\displaystyle \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 $\displaystyle \frac{x}{11} = \cosh t$ .... - Feb 3rd 2008, 02:33 AMplayer07
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. - Feb 3rd 2008, 07:22 AMbobak
He really didnt misunderstnad you.

You have misunderstood him! - Feb 3rd 2008, 10:07 AMplayer07
thank you for you help :)