Consider the following:
∬_D x dA, D is enclosed by the lines y = x, y = 0, x = 2
Express D as a region of type I.
D = {(x, y) | y ≤ x ≤ 2, 0 ≤ y ≤ x}
D = {(x, y) | 0 ≤ x ≤ 2, 0 ≤ y ≤ x}
D = {(x, y) | 0 ≤ x ≤ y, 0 ≤ y ≤ x}
D = {(x, y) | 0 < x < y, 0 < y < x}
D = {(x, y) | 0 ≤ x ≤ y, 0 ≤ y ≤ 2}
Express D as a region of type II.
D = {(x, y) | 0 ≤ y ≤ x, 0 ≤ x ≤ y}
D = {(x, y) | 0 ≤ y ≤ 2, y ≤ x ≤ 2}
D = {(x, y) | 0 ≤ y ≤ x, y ≤ x ≤ 2}
D = {(x, y) | 0 ≤ y ≤ 2, 0 ≤ x ≤ y}
D = {(x, y) | 0 ≤ y ≤ 2, 0 ≤ x ≤ 2}
Evaluate the double integral in two ways: