What is the arc length of the curve given by r(t)=(4t,3t-6)r(t)=(4t,3t6) in the interval t in [0,7]t[0,7]?

1 Answer
Nov 25, 2016

35

Explanation:

The Arc Length of f(t)=(x(t), y(t) ) is given by:

L = int_a^bsqrt((dx/dt)^2 + (dy/dt)^2)dt

Let x(t)=4t => dx/dt=4
And, y(t)=3t-6=>dy/dt=3

So,

L = int_0^7sqrt((4)^2 + (3)^2)dt
:. L = int_0^7sqrt(16+9)dt
:. L = int_0^7sqrt(25)dt
:. L = 5int_0^7 dt
:. L = 5[t]_0^7
:. L = 5(7-0)
:. L = 35