Question

Find the arc length of: y=3/2(x)^(2/3), x=[1,8]. I used the equation L(c)=(1+(f'(x))^2)^(1/2) and did a u-sub for what I got: (1+x^(-2/3))^(1/2) and got du-3x^(5/3)/2=dx. I ended up getting something like -[x^(5/3)+x] before plugging in [1,8], which is wrong. I have no idea where to begin fixing this nonsense.

Answer 1

\[y\ =\ \frac{3}{2}x^{\frac{2}{3}}\]??