What is the length of the path along the graph of y equals the square root of the quantity 16 minus x squared between x = 2 and x = 4?

Question

What is the length of the path along the graph of  between x = 2 and x = 4?

A
B
C
D

Answer 1

s = ∫₂⁴(1 + y'²)^1/2dx; y' = 1/2(16 - x²)^-1/2(- 2x) = - x/16 - x²)^1/2;

s = ∫₂⁴[(1 + x²/(16 - x²)]^1/2dx = 4∫₂⁴1/(16 - x²)^1/2dx = 4sin^-1(x/4)₂⁴ = 4(sin^-11 - sin^-11/2) = 4(π/2 - π/6) = 4π/3

Answer is B