求曲线√x+√y=√a与两坐标轴所围成的面积

问题描述:

求曲线√x+√y=√a与两坐标轴所围成的面积

56.575

y = (√a - √x)² = a - 2√(ax) + x 0 ≤ x ≤ √aS = ∫(a - 2√(ax) + x)dx (0 ≤ x ≤ √a)= (ax -(4√a/3)x³/² + x²/2)= a³/² - (4/3)a⁵/⁴ + a/2