integral (proof/showing)

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November 17th 2010, 07:11 AM
rlkmg

integral (proof/showing)

Having a bit of trouble, here is what i've done so far.
November 17th 2010, 08:13 AM
tonio

Quote:

Originally Posted by rlkmg

Having a bit of trouble, here is what i've done so far.

So...?? What do you think you've proved so far?

$\displaystyle{I_{n+1}:=\int\limits^1_0\frac{x^n}{2-x}\,dx=\int\limits^1_0\frac{x^{n-1}(2-(2-x))}{2-x}\,dx=2I_n-\int\limits^1_0x^{n-1}\,dx}$ , and we're done

Tonio
November 17th 2010, 11:11 AM
rlkmg

Quote:

$\int\limits^1_0x^{n-1}\,dx}$

thanks, I've got it now (the 2I(n) ) bit, but how do i get the above part to 1/n?
November 17th 2010, 12:56 PM
tonio

Quote:

Originally Posted by rlkmg

thanks, I've got it now (the 2I(n) ) bit, but how do i get the above part to 1/n?

Just solve it!

Tonio
November 17th 2010, 01:12 PM
rlkmg

ahh okay, got it now, thanks! silly, didnt see that :)

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