Integration by parts help (1 Viewer)

[YBK]

Hey, for integration by parts I always get up to the same step but can't keep going.

It's where you gotta sub the "I" thing back into the equation.

for example, here's a question from the 2005 CSSA paper that I can't do.

Q2) e)i) If In = integral between 1 and 0 of x(1-x)^n

show that In = {n/(n+2)}In-1

I've got the solutions but it's this step that I can't figure out:

n/2 . integral between 1 and 0 of {(1-x) - 1} x (1-x)^(n-1) dx
and then in the next line they sub in the In

I dont get either of those two steps...

it's always here where I get confused

thanks for any help!!!

 

[Riviet]

Expand it:

{(1-x) - 1} x (1-x)^(n-1) = x(1-x)(1-x)^n-1 - x(1-x)^n-1
=x(1-x)ⁿ - x(1-x)^n-1

Notice that the first bit forms your I_n and the second bit forms your I_n-1.

P.S Post your trial related questions in the trial revision thread!

 

[YBK]

yay! I undertand! thanks Riviet!