How to Draw the plane curve and find its length in the given interval?

#r(t)=i+t^2j+t^3k,[0,2]#

1 Answer
Apr 14, 2018

See below

# s = 8/27 (10 sqrt(10) - 1)#

Explanation:

In terms of drawing the curve, good luck with that! I have no access to suitable software and cannot help.

In terms of it's length:

#s = int_(Delta t) \ dot s \ dt \ qquad square#

#dot s = sqrt (mathbf v * mathbf v)= sqrt (mathbf r' * mathbf r')#

#mathbf r' = [0, 2t, 3t^2]^T#

#dot s = t sqrt (4 +9 t^2 )#

Using #square#:

#s = int_0^2 \ t sqrt (4 +9 t^2 ) \ dt = [1/27 (9 t^2 + 4)^(3/2)]_0^2#

# = 8/27 (10 sqrt(10) - 1)#