Question

Find the arc length of the following curve on the given interval. x equals 12 t minus 5 comma y equals 16 t plus 3 ​, 0 less than or equals t less than or equals 4 The length of the curve is 80 .

Answer 1

Answer:

80

Step-by-step explanation:

We are given:

$x(t) = 12t-5\\y(t) = 16t+3\\0\leq t\leq4$ ⇒ $[\alpha,\beta] = [0,4]$

To find arc length, we will use the following formula,

$\int\limits^\beta_\alpha\sqrt{(\frac{dx}{dt})^2+\frac{dy}{dt})^2}\:dt=\int\limits^4_0\sqrt{12^2+16^2}\:dt=20t|^4_0 = 20*(4-0)=80$