Let C denote the set of points that are interior to, or on the boundary of, a square with opposite vertices at the points (0, 0) and (1, 1). Let Q(C) = ∫ ∫_C dy dx.
(a) If C ⊂ C is the set {(x, y) : 0 < x < y < 1}, compute Q(C).
(b) If C ⊂ C is the set {(x, y) : 0 < x = y < 1}, compute Q(C).
(c) If C ⊂ C is the set {(x, y) : 0 < x/2 ≤ y ≤ 3x/2 < 1}, compute Q(C).