Step-by-step explanation:
Using arc length formula for parametric equations:
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
L = ∫₀² √((3t²)² + (-2t)²) dt
L = ∫₀² √(9t⁴ + 4t²) dt
L = ∫₀² t√(9t² + 4) dt
If u = 9t² + 4, then du = 18t dt, or 1/18 du = t dt.
When t = 0, u = 4. When t = 2, u = 40.
L = 1/18 ∫₄⁴⁰ √u du
L = 1/18 (⅔ u^(³/₂)) |₄⁴⁰
L = 1/27 (u√u)|₄⁴⁰
L = 1/27 (40√40 − 4√4)
L ≈ 9.07
Your answer is correct!
