What is the arc length of the curve given by #r(t)=(4t,3t-6)# in the interval #t in [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 #
