Integration 积分

The meaning of $\int$

$\int$ is kind of like $S$ in $sum$.

$\int_1^4 x$ is different than $\sum_{n=1}^{4} n$.

In $\sum_{n=1}^{4} n$, n can only be increased by 1. So it will be $1 + 2 + 3 + 4$.

But in $\int_1^4 x$, $x$ can be any number in interval $[1, 4]$, $dx$ is another conception that not related in this $x$. So it will be $1 + ... + 2 + ... + 3 + ... + 4$