First step?The solid lies between planes perpendicular to the x axis at $\displaystyle x = 0$ and $\displaystyle x = 4$. The cross-sections perpendicular to thexaxis on the interval $\displaystyle 0 \leq x \leq 4$ are squares whose diagonals run from the parabola $\displaystyle y = -\sqrt{x}$ to the parabola $\displaystyle y = \sqrt{x}$. Find the volume

$\displaystyle V = \int_{a}^{b} A(x) dx$

$\displaystyle x^{2}$ is the area of a square

$\displaystyle A = x^{2}$

$\displaystyle V = \int_{0}^{4} [2 \sqrt{x}]^{2} dx$

$\displaystyle V = \int_{0}^{4} 4x dx$

$\displaystyle V = \dfrac{4x^{2}}{2}$

$\displaystyle V = 2x^{2}$

$\displaystyle V = [2(4)^{2}] - [2(0)^{2}] $

$\displaystyle V = [32] - [0] = 32 $ The book says the answer is 16. Something went wrong here.