What does $\frac{x^3}{9}\bigg|_0^1$ mean, and how should it be spoken?

Question

$$\frac{x^3}{9}\Bigg|_0^1$$ The vertical line above: what does it mean, and how would I state this whole structure in spoken words, so that a screen reader would be able to read it aloud correctly?

Answer 1

The vertical line means evaluate it from the top to the bottom.

So say $x^3/9$ from $0$ to $1$.

in general $f(x)\biggr \vert^b_a$ would be $f(b)-f(a)$, in this case:

You would evaluate it as $(1)^3/9 - (0)^3/9$.

Basically just evaluate the expression with $x=$ top limit and the bottom limit, subtract the bottom expression from the top expression.

Answer 2

It is the standard notation for describing the limits of an integral.

As well mentioned in comments and other answers, $f(x)\biggr \vert^b_a$ is same as $f(b)-f(a)$ and here $a$ and $b$ are called limits of the integral or the integral is said to be over the interval $[a,b]$ .

When you write something like $\frac{x^3}{9}\Bigg|_0^1$ you are gonna say it as

Evaluate $\frac{x^3}{9}$ over the interval $[0,1]$ or evaluate $\frac{1^3}{9}-\frac{0^3}{9}$.

Answer 3

It looks like people have already told you what to do mathematically. I'm a math tutor, and what I say out loud is

"x cubed over nine, evaluated from one to zero."