Given $f(x,y)$ is a continuous function, Do these integrals equal? Given range $\{ 0 \le x \le 1, 0 \le y \le 1\}$
Do these integrals equal?
$\int_0^1(\int_0^y f(x,y)dx)dy = \int_0^1(\int_0^x f(x,y)dy)dx$
Well, the answer is no. It seems like the triangulars are different in LHS, RHS.
I don't understand $ (D_2)$. Here: $D_1 = \{(x,y) | 0 \le x \le 1, 0 \le y \le x\}$,
but why $D_2 = \{(x,y) | 0 \le x \le 1, x \le y \le 1\}$ ?
Especially this part of $D_2: x \le y \le 1$.

Figure of Changing order of integration

