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 $\displaystyle (4-x^2)^n$ as $\displaystyle (4-x^2)(4-x^2)^{n-1}$ then expand so we have:
$\displaystyle I_n=\int_0^2 (4-x^2)^n dx = 4I_{n-1}-\int_0^2 [x]~[x(4-x^2)^{n-1}]dx$
Now use integration by parts on the integral on the right (you will get a multiple of $\displaystyle I_n$ )
RonL