How do you find the arc length of the curve f(x)=2(x-1)^(3/2) over the interval [1,5]?
1 Answer
May 16, 2018
Use the arc length formula.
Explanation:
f(x)=2(x−1)^(3/2)
f'(x)=3sqrt(x-1)
Arc length is given by:
L=int_1^5sqrt(1+9(x-1))dx
Simplify:
L=int_1^5sqrt(9x-8)dx
Integrate directly:
L=2/27[(9x-8)^(3/2)]_1^5
Hence:
L=2/27(37^(3/2)-1)