Question

Find the arc length of the curve on the given interval. Parametric Equations Interval x = 6t + 5, y = 7 − 5t −1 ≤ t ≤ 3

Answer 1

Answer:

31.241

Step-by-step explanation:

x = 6t + 5,   y = 7 − 5t            −1 ≤ t ≤ 3

dx/dt = 6

dy/dt = -5

The arc length of the curve can be calculated below as

L = ∫$\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt})^2 dt }$

 = $\int\limits^3_ {-1} \, \sqrt{36 + 25 dt}$

 = $\sqrt{61} \int\limits^3_ {-1} \, dt$

 = $\sqrt{61} [3-(-1)]$

= 4$\sqrt{61}$  = 31.241