This problem is from mathematical statistics 8ed by hogg
Let $C = \mathbb R^n$ For $A$ in $C$ define the set function
$$ Q(A) = \idotsint\limits_A dx_1 dx_2 \cdots dx_n$$
If $B = \{(x_1, x_2, \dots, x_n) : 0\leq x_1 \leq x_2 \leq \cdots \leq x_n \leq 1\}$ then, $$Q(B) = \text{?}$$
I thought $Q(B)$ is $$Q(B) = \int_{x_{n-1}}^1 \left[ \int_{x_{n-2}}^{x_n} \cdots \left[ \int_{x_1}^{x_3} \left[ \int_0^{x_2} dx_1 \right] dx_2 \right] \cdots dx_{n-1} \right] dx_n $$
Because $$0\leq x_1 \leq x_2 \quad \text{so} \quad \int_0^{x_2}dx_1$$ $$x_1\leq x_2 \leq x_3 \quad \text{so} \quad \int_{x_1}^{x_3}dx_2$$ $$ \vdots$$ $$x_{n-1}\leq x_n \leq 1 \quad \text{so} \quad \int_{x_{n-1}}^1 \, dx_n$$
But answer is $$Q(B) = \int_0^1 \left[ \int_0^{x_n} \cdots \left[ \int_0^{x_3} \left[ \int_0^{x_2} dx_1 \right] dx_2 \right] \cdots dx_{n-1} \right] dx_n $$
I can't understand why lower ranges of each integral are $0$?
please help me