reduction formula for J[k] = int((x^2-121)^k, x = 0 .. 11)

[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)

or give me a hint

thanks in advance

 

[galactus]

You can do this via the gamma function.

\(\displaystyle \int_{0}^{11}(x^{2}-11^{2})^{k}dx=\frac{1}{2}\left[\frac{11^{2k+1}\cdot{(-1)^{k}}\cdot{\sqrt{\pi}}\cdot{{\Gamma(k+1)}}}{{\Gamma}(k+\frac{3}{2})}\right]\)

 

[player07]

Hi glactus, can you find another way to find the answer beacause i didn't have studied the gamma formula yet
it will be cool if you can do that beacause i realy need the solution
thank you very much in advance

 

[galactus]

The solution I gave is as good as any. I would suggest studying the gamma function then :wink: It comes in handy for more advanced integration. Why were you given such a problem?.

BTW, I got that solution from Maple. That is what technology is for.