Let the plane figure d be bounded by the square of the curve y = x, the straight lines X = 1 and y = 0, and find the area s of D

Let the plane figure d be bounded by the square of the curve y = x, the straight lines X = 1 and y = 0, and find the area s of D

1) Let f (x) = x * x / 3F '(x) = y = x * x, that is, the derivative of F (x) is y = x * x, s = y | 0_ 1 = f (1) - f (0) = 1 / 32) so that DX = 1 / N, n tends to infinity, s is transformed into the area of each small rectangle, that is, s = DX * Y1 + DX * Y2 +... DX * yn = DX * (DX * DX) + DX * (2DX * 2DX) + DX * (3DX * 3DX +... + DX * (n