The problem is y=x^(2/3) and x=1 and x=8. I need to find the exact arc length of the curve over the interval.
The formula used is the arc length formula: L=integral from a to b of (1+(dy/dx)^2) ^(1/2)
So far I got this:
Integral from 1 to 8 of (1+(4/9*x^(-2/3)))^(1/2)dx
I don't know how to integrate this. Is it a u substitution? I tried u= 1+ 4/9x^(-2/3) and I have an x^(-5/3) left over so that won't work.