1. Find the length of arc of the curve y = (x ^ 2)/8 - ln(x) from x = 3 to x = 9 .

Answer 1

S = ∫₃⁹(1 + (x/4 - 1/x)²)^1/2dx = ∫₃⁹(x/4 + 1/x)dx = (x²/8 + lnx)₃⁹ = 81/8 + ln9 - 9/8 - ln3 = 9 + ln3 = 10.1