Answer :
The arc length of the curve on the given interval is 31.241.
Explain the term Parametric Equations?
- Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are characterized as continuous functions of a parameter and independent of other variables.
Parametric Equations
- x = 6t + 5,
- y = 7 − 5t
Interval: −1 ≤ t ≤ 3
dx/dt = d/dx(6t + 5)
dx/dt = 6
And, dy/dt = d/dt(7 − 5t )
dy/dt = -5
The arc length of curve is estimated as;
L = ∫√(dx/dt)² + (dy/dt)²).dt
L = ∫√(36 + 25t) Interval: [−1 ≤ t ≤ 3]
L = √61 x (3 + 1)
L = 31.241
Thus, the arc length of the curve on the given interval is 31.241.
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