Finding the height of a Pyramid where the sides are given by an equation

Problem:

The vertex of a pyramid lies at the origin, and the base is perpendicular to the x-axis at $x = 4$. The cross sections of the pyramid perpendicular to the x-axis are squares whose diagonals run from the curve $y = -5x^2$ to the curve $y = 5x^2$. Find the volume of the pyramid.

Answer:

The first step is to graph the two curves. A graph can be found at the following URL:
https://www.wolframalpha.com/input/?i=plot+5x%5E2+%2C+-5x%5E2

Since the cross sections of the pyramid are perpendicular to the x-axis we will integrate with respect to x. Since each cross section is a square and $y$ goes from $-5x^2$ to $5x^2$, the the length of one side of the square will be $5x^2 – (-5x^2)$ or
$10x^2$. Let $V$ be the volume we are looking for.
begin{align*}
du &= -dx \
V &= int_0^4 (10x^2)^2 ,,, dx = int_0^4 100x^4 ,,, dx \
V &= frac{100x^5}{5} Big|_0^4 = 20x^5 Big|_0^4 \
V &= 20(4^5) = 20(1024) = 20480
%
end{align*}
The book’s answer is:
$$ 10,240 $$
Where did I go wrong?