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

80

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{((dx)/(dt))^2+(dy)/(dt))^2}\:dt=\int\limits^4_0√(12^2+16^2)\:dt=20t|^4_0 = 20*(4-0)=80`