Find the arc length of the graph of the equation y+1/4x+x^3/3=0 from the point(2,67/24) to point(3,102/12) help me with this thanx!
Ok. Using parentheses to disambiguate the function, we have
y = 1/(4x) + x^3/3
y' = -1/(4x^2) + x^2
so, the arc length is
∫[2,3] √(1+(y')^2) dx
= ∫[2,3] √(1+(-1/(4x^2) + x^2)^2) dx
= ∫[2,3] x^2 + 1/(4x^2) dx
= 1/3 x^3 - 1/(4x) [2,3]
(1/3*27 - 1/12)-(1/3 * 8 - 1/8)
= 51/8