Find the Arc-length of the curve: y=1/3x^3/2 - x^1/2 ; 1 ≤ x ≤ 9

Question

Find the Arc-length of the curve: y=1/3x^3/2 - x^1/2 ; 1 ≤ x ≤ 9

If possible please explain the step by step process in a video.

Answer 1

Arc length L = ∫₁⁹√[1 + (1/2x^1/2 - 1/2x^-1/2)²]dx = ∫₁⁹1/2(x^1/2 + x^-1/2)dx = 1/2(2/3x^3/2 + 2x^1/2)₁⁹ =

1/2[(18 + 6) - (2/3 + 2)] = 32/3

Answer 2