Use your graph to find the surface area numerically

Question

x^1/2 + y^1/3 = 3, 1 ≤ x ≤ 4; x-axis

Answer 1

y = (3 - x^1/2)³; y = - 3(3 - x^1/2)²/(2x^1/2).

Surface area S = 2π∫₁⁴y√1 + y'²dx = 2π∫₁⁴[(3 - x^1/2)³√1 + 9(3 - x^1/2)⁴/(4x)]dx = 210.415