# arc length and parameterized curve length

• Dec 3rd 2008, 09:22 PM
covette
arc length and parameterized curve length
help would be much appreciated becasue i have been trying and cannot find out how to do these two problems.

1) Find the length of parametrized curve given by
x(t) = 0t^3-3^2+6t, y(t)= -1t^3+3t^2+0t t from 0 => 1

and i know L = integral (0 to 1) sqrt( (-6t+6)^2 + (-3t^2+6t) )

but do not know how to proceed through the integral and all..

and 2) Find the length of the arc formed by
x^2 = 10y^3
from point A to point B where, A = (0,0) and B = (100,10)

no idea where to go on that one and help ASAP would be great seeing as its due soon.

thank you once again for any help
• Dec 5th 2008, 02:33 AM
mr fantastic
Quote:

Originally Posted by covette
help would be much appreciated becasue i have been trying and cannot find out how to do these two problems.

1) Find the length of parametrized curve given by
x(t) = 0t^3-3^2+6t, y(t)= -1t^3+3t^2+0t t from 0 => 1

Mr F says: I can't understand the expressions you've posted for x(t) and y(t). Please clarify.

and i know L = integral (0 to 1) sqrt( (-6t+6)^2 + (-3t^2+6t) )

but do not know how to proceed through the integral and all..

and 2) Find the length of the arc formed by
x^2 = 10y^3
from point A to point B where, A = (0,0) and B = (100,10)

no idea where to go on that one and help ASAP would be great seeing as its due soon.

thank you once again for any help

2) Start by differentiating $y = \left( \frac{x^2}{10}\right)^{1/3}$ and substitute into the usual formula.