y = 2 - x
√x = 2 - x
平方：x² - 5x + 4 = 0
(x - 4)(x - 1) = 0
x = 1, y = 1, 交点A(1, 1)
x = 4, y = -2 (舍去)
y = 2 - x和x轴的交点为B(2, 0)
(1)
S =∫₀¹√xdx +∫₁²(2-x)dx
= (2/3)x^(3/2)|₀¹ + (2x - x²/2)|₁²
= 2/3 + 1/2
= 7/6
(2)
该旋转体在x处的截面积：
(i) 0 < x < 1:
s =π(√x)² = πx
这部分体积V1 = ∫₀¹πxdx = π*x²/2|₀¹ = π/2
(ii) 1 < x < 2:
s = π(2 - x)² = π(4 - 4x + x²)
这部分体积V2 = ∫₁²π(4 - 4x + x²)dx = π(4x - 2x² + x³/3)|₁²
= π/3
V = V1 + V2 = π/2 + π/3 = 5π/6
