Please Help, I'll give 5 star rating
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Arc length = ∫√(1 + (dy/dx)^2) dx from 1 to 3
dy/dx = (3/2)*4 * x^(1/2) = 6*x^(1/2)
Arc length = ∫√(1 + (6*x^(1/2))^2) dx from 1 to 3
= ∫√(1 + 36x) dx from 1 to 3
Let z = 1 + 36x => dz/36 = dx
1/36 * ∫√z dz from 37 to 109
= 1/54 * (109^(3/2) - 37^(3/2))
dy/dx = (3/2)*4 * x^(1/2) = 6*x^(1/2)
Arc length = ∫√(1 + (6*x^(1/2))^2) dx from 1 to 3
= ∫√(1 + 36x) dx from 1 to 3
Let z = 1 + 36x => dz/36 = dx
1/36 * ∫√z dz from 37 to 109
= 1/54 * (109^(3/2) - 37^(3/2))