Two questions from calc II

hey guys, thanks to those who helped me on my last problem, this time i've ufortunately got two :(

1) for the integral x

trap(10)= 12.676

trap(30)= 10.420

i have to find the actual value

the error is n^2 when using trap so 20^2= 400, 12.676-10.420 = 2.256

so is x = 2.256/400?

i'm not really sure how to go about this

2) this problem i don't really have any idea what to do whatsoever, and it's a proof (which are gods way of punishing those you take math classes)

i need to integrate R(x) = t^(x-1)e^(-t)dt from zero to infinity

then prove that R(x+1) = nRn

i tried working out the anitderivate for the start, and i came out with just (t^(x+1)e^(-t)) / ln(t)

i'm not really even sure if that is correct

thanks in advance to anyone who can help me