第1个回答 2013-02-14
解两曲线得交点(0,0),(1,1)
面积 = ∫(0→1) (√x - x²) dx
= (2/3)x^(3/2) - x³/3 |(0→1)
= 2/3 - 1/3
= 1/3
体积 = 2π∫(0→1) x(√x - x²) dx,柱壳法
= 2π∫(0→1) [x^(3/2) - x³] dx
= 2π • [(2/5)x^(5/2) - x⁴/4] |(0→1)
= 2π • (2/5 - 1/4)
= 3π/10
或体积 = π∫(0→1) [(√y)² - (y²)²] dy,盘旋法,这个做验算
= π∫(0→1) (y - y⁴) dy
= π • (y²/2 - y⁵/5) |(0→1)
= π • (1/2 - 1/5)
= 3π/10本回答被网友采纳