# 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 #