Find the arc length of x=(y-1)^3/2 from the point (0,1) to (8,5) give an exact answer.

Question

I have been stuck on this question for two days cans someone please help.

Answer 1

You know that
s = ∫ √(1 + x'^2) dy
so that would be
∫[1,5]√(1 + (3/2 √(y-1))^2) dy
= ∫[1,5]√(1 + 9/4 (y-1)) dy
= 1/2 ∫[1,5]√(9y-5) dy = 8/27 (10√10 - 1)