Arc Length Problem?

Here's the Problem:

Find the arc length of y = [(x^3)/6] + [1/(2x)] on [0.5,2]

I struggling with the algebra on this problem, can anyone be kind enough to help?

Note: I cannot use any form of integration techniques other than U-Subsitution or just taking the antiderivative. Cannot use trig sub, integration by parts, or partial fractions decomposition. These are in the next chapter. Thank You

1 Answer
Mar 27, 2018

33/163316

Explanation:

Given y = x^3/6+1/(2x)y=x36+12x we have

y'=x^2/2-1/(2x^2) and

ds = sqrt(1+(dy/dx)^2)dx = 1/2(sqrt(2 + 1/x^4 + x^4)) dx= 1/2(x^2+1/x^2)dx

and

s = int_(1/2)^2 1/2(x^2+1/x^2)dx = 33/16