# Thread: Reduction formulae help!

1. ## Reduction formulae help!

Hi everyone I need your help. This is a question of using reduction formulae. This was adapted from Further Pure 2.

(I don't know how to type equations here, so I will upload as a picture)

Thanks for your help!

2. Originally Posted by rednest
Hi everyone I need your help. This is a question of using reduction formulae. This was adapted from Further Pure 2.

(I don't know how to type equations here, so I will upload as a picture)

Thanks for your help!
Integration by parts:

first write $(4-x^2)^n$ as $(4-x^2)(4-x^2)^{n-1}$ then expand so we have:

$I_n=\int_0^2 (4-x^2)^n dx = 4I_{n-1}-\int_0^2 [x]~[x(4-x^2)^{n-1}]dx$

Now use integration by parts on the integral on the right (you will get a multiple of $I_n$ )

RonL