What is the arc length of the curve given by r(t)=(4t,3t-6)r(t)=(4t,3t−6) in the interval t in [0,7]t∈[0,7]?
1 Answer
Nov 25, 2016
35
Explanation:
The Arc Length of
L = int_a^bsqrt((dx/dt)^2 + (dy/dt)^2)dt
Let
And,
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