How to read expressions with mathematical symbols

Question

(I'm not a native English speaker) When I meet various compositions of mathematical symbols in a book, I pause some time to read them. Also, I don't know that my way of reading them is correct or not.

For example, there are five mathematical expressions.

1. $\int_a^b f(x) dx$

2. $\prod_{\alpha \in J} X_\alpha$

3. $\sum_{i=1}^\infty \mu(E_i)$

4. $\bigcup_{x\in U} B_x$

My reading method is

1) Integral from $a$ to $b$ $f(x) dx$

2) Product from alpha in $J$ $X$ sub alpha

3) Sum from $i$ is $1$ to infinity mu $E$ sub $i$

4) Union from $x$ in $U$ $B$ sub $x$

Could you give me some advice on how to read expressions like these?

Answer 1

I'm a native english speaker. I'd read these as

• Integral from $a$ to $b$ of $f ~ dx$.

• Product over $\alpha$ in $J$ of $X$ sub $\alpha$.

• Sum from $i$ equals $1$ to infinity of $\mu$ of $E$ sub $i$.

• Union over $x$ in $U$ of $B$ sub $x$.

Answer 2

Native English speaker from the US. I vary some of my verbal math. For example, I may read infinite sums and products like $\sum_{j=1}^\infty a_j$ as "The sum, over $j$, of 'a-j'." I ignore saying "sub" now.

In short sum, multiply, and integrate over indices.

Each person is different and your way is just fine.