Answer
$0 \leq \iint_{T} \sin^4(x+y) dA \leq 1 $
Work Step by Step
When $m \leq f(x,y) \leq M$ on the region $S$, then we have:
$m \cdot A \leq \iint_{S} f(x,y) d A \leq M \cdot A .....(1)$
and $A$ represents the area of the region $S$.
The area of a triangle with base $1$ and height $2$ is given as: $A =\dfrac{1}{2} (1)(2)=1$
Since, $0 \leq \sin^4(x+y) \leq 1$
Therefore, $0 \cdot A(T) \leq \iint_{T} \sin^4(x+y) dA \leq 1 \cdot A(T) $
So, we have: $0 \leq \iint_{T} \sin^4(x+y) dA \leq 1 $
