Calculus of a Single Variable, Chapter 10, 10.3, Section 10.3, Problem 45

The formula of arc length of a parametric equation on the interval alt=tlt=b is:
L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt
The given parametric equation is:
x=3t + 5
y=7 - 2t
The derivative of x and y are:
dx/dt = 3
dy/dt = -2
So the integral needed to compute the arc length of the given parametric equation on the interval -1lt=tlt=3 is:
L = int_(-1)^3 sqrt(3^2+(-2)^2) dt
The simplified form of the integral is:
L = int_(-1)^3 sqrt13 dt
Evaluating this yields:
L = sqrt13t |_(-1)^3
L = sqrt(13)*3 - sqrt13*(-1)
L=3sqrt13 + sqrt13
L=4sqrt13
Therefore, the arc length of the curve is 4sqrt13 units.