length curve calculus

Question

Determine the length of the curve y(x) = 1/4x²-1/2ln(x) on the interval (1,2)

Answer 1

It appears that the equation should look as follows: y(x)= x²/4 - lnx/2. If that is the case L= ∫₁²√(1+(y')² dx where y' is x/2-1/2x and (y')² =x²/4 -1/2 +1/(4x²) and so the equation for L=∫₁²√(1 +x²/4 -1/2 +1/(4x²))dx and L=∫₁²√(x²/4 +1/2 +1/(4x²))dx and L= ∫₁²√( x/2 + 1/(2x))²dx and so L= ∫₁²(x/2 + 1/(2x))dx L= (x²/4 + lnx/2)₁² L=4/4 +ln2 /2 -1/4 -ln1 /2 = 3/4 +ln2 /2.