# Thread: arc length and parameterized curve length

1. ## 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

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