Question

Find the length of the arc formed by
y = (1/8)(4x^2-2ln(x)) from x=4 to x=8.

I found the derivative of the function and got y'= x-(1/4x)

Where I'm lost now is after plugging it into the arc length equation: integral of sqrt(1+(x-(1/4x))^2). Squaring the derivative yields me sqrt(1+x^2+1/16x-1/2). Help please.

Answer 1

I got sqrt [ 1 + x^2 -(1/2) + 1/(16x^2) ]
which is
sqrt [ x^2 + (1/2) +1/(16x^2) ]
BUT
x^2 + (1/2) + 1/(16x^2) = [x+ 1/(4x)]^2
ok ?

Answer 2

Oh yes, sorry, I merely had a typo. I had the same result as you. What I'm confused about is what to do from that point on.

Answer 3

well, the sqrt of that is just
x + (1/4)(1/x)
integral of that is
(1/2) x^2 + (1/4) ln x