I'm not sure where my instructor was going with this problem. Can anyone help?

Question

In length units, correct to the nearest thousandth, find the arc length of the curve segment y = x^5 from (0, 0) to (1, 1) .

Answer 1

the arc length differential is da^2=dx^2+dy^2. divide RHS by dx^2 and square root both sides to get

ds=sqrt(1+(dy/dx)^2)

so y(x)= x^5 => dy/dx=5x^4

so to get arc length we integrate ds with respect to x with limits x= 0 to x= 1

integral from 0 to 1 of sqrt(1+25x^8) with respect to x

since a rounded answer is required i assume you must use a numerical scheme such as Simpson's rule to obtain answer but again the integrand is sqrt(1+25x^8) limits x= 0 to 1