I got this problem: "Which approximation, $z_2$ do you get when doing one step of Newtons method on $f(x) = 0$ to approximate the unlinear equation $ f(z) = \int_{-1}^1 z^2x^2 dx - 1$. You should use the trapezoidal rule with h = 1 and start with $z_1 = 3$ ".
Okay, I'm assuming that I should do: $ z_2 = z_1 - \frac {\int_{-1}^1 z^2x^2 dx - 1} {f'(z)}$. Is that correct?
If so, my problem is first of all: How do i find the derivative? I only know how to to do it with an integral that has a x as the upper bound.
Moreover, do I replace z within the integral with $z = 3$. I.e: is $z$ within the integral the same as $z_1$?