Question

Consider the parametric equation `x = 9(cost+tsint)` and `y = 9(sint-tcost)`, What is the length of the curve for `t= 0` to `t=3pi/10`?

Answer 1

`9/2((3pi)/10)^2`

Explanation:

We have

`{(dx/dt=9tcost),(dy/dt=9tsint):}`

and

`(ds)/dt=sqrt((dx/dt)^2+(dy/dt)^2) = 9t`

then

`s=int_(t=0)^(t=(3pi)/10)9tdt = 9/2((3pi)/10)^2`