how would you integrate the general binomial expansion??

http://www.mathhelpforum.com/math-he...2c215de0-1.gif

thanks for and help

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- Dec 10th 2008, 09:03 AMhmmmmintegration of binomial expansion
how would you integrate the general binomial expansion??

http://www.mathhelpforum.com/math-he...2c215de0-1.gif

thanks for and help - Dec 10th 2008, 11:33 AMfobos3
$\displaystyle \int (a\times x+b)^n \, dx=\frac{(a x+b)^{n+1}}{a(n+1)}$

If $\displaystyle F (x) = \int f(x)dx$ then:

F(ax+b)=F(x)/a - Dec 10th 2008, 02:15 PMhmmmmthanks
thanks but i was more asking how you would integrate the right hand side of the equation? sorry

- Dec 10th 2008, 02:39 PMMathstud28
- Dec 11th 2008, 12:46 PMhmmmmthanks
so how do we integrate this?

- Dec 11th 2008, 01:20 PMGreengoblin
$\displaystyle \sum_{k=0}^{n} {n\choose{k}}x^{n-k}y^k$

$\displaystyle = x^n+nx^{n-1}y+\frac{n(n-1)}{2!}x^{n-2}y^2+\cdots +\frac{n(n-1)\cdots(n-r+1)}{r!}x{n-r}y^r+\cdots+y^n$

So taking:

$\displaystyle \int\sum_{k=0}^{n}{n\choose{k}}x^{n-k}y^kdx$

Is just a case of using the addition and power rules for integrals on this series.