切線與x軸的交點為B(-1, 0), 與y軸的交點為C(0, 1/2)
切線(y = (x+1)/2)與拋物線和坐標(biāo)軸所圍的區(qū)域分別為綠色和紫色.
繞x軸旋轉(zhuǎn)一周,在x處截面積為:
f(x) = π[(x+1)/2]² = π[(x+1)²/4 (-1 ≤ x < 0)
= π[(x+1)/2]² - π(√x)² = π[(x+1)²/4 - πx = π[(x-1)²/4 (0 ≤ x ≤ 1)
V = ∫ π(x+1)²dx/4 (從-1到0)
+ ∫ π[(x-1)²dx/4 (從0到1)
= (π/4)∫ (x+1)²d(x+1) (從-1到0)
+ (π/4)∫ (x-1)²d(x-1) (從0到1)
= π(x+1)³/12 (從-1到0)
+ π(x-1)³/12 (從0到1)
= π/12 + π/12
= π/6
