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 = ∫[tex]\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt})^2 dt }[/tex]
= [tex]\int\limits^3_ {-1} \, \sqrt{36 + 25 dt}[/tex]
= [tex]\sqrt{61} \int\limits^3_ {-1} \, dt[/tex]
= [tex]\sqrt{61} [3-(-1)][/tex]
= 4[tex]\sqrt{61}[/tex] = 31.241
