Set up, but do not evaluate, the integral that represents the length of the curve given by x = t - t2, y equals 4 thirds times t raised to the 3 halves power , over the interval 1 ≤ t ≤ 2

Question

Set up, but do not evaluate, the integral that represents the length of the curve given by

x = t - t²,  , over the interval 1 ≤ t ≤ 2

Answer 1

x = t - t²; y = 4/3t^3/2, 1 ≤ t ≤ 2;

Length of curve s = ∫₁²[(1 - 2t)² + (2t^1/2)²]^1/2dt = ∫₁²(1 + 4t²)^1/2dt