Help with reduction formula

**player07** · February 2nd 2008, 02:03 PM

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

**mr fantastic** · February 2nd 2008, 04:23 PM

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 $\frac{x}{11} = \cosh t$ ....

**player07** · February 3rd 2008, 02:33 AM

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

can you look again to the question please.

**bobak** · February 3rd 2008, 07:22 AM

He really didnt misunderstnad you.
You have misunderstood him!

**player07** · February 3rd 2008, 10:07 AM

thank you for you help

Thread: Help with reduction formula

LinkBack

Thread Tools

Display

Help with reduction formula

Similar Math Help Forum Discussions

Sin reduction formula!

reduction formula

Using a Reduction Formula

Reduction formula

Reduction Formula

Search Tags