Question

Consider the parametric equation `x= 10(cost+tsint)` and `y= 10(sint-tcost)`, What is the length of the curve from `0` to `((3pi)/2)`?

Answer 1

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

Explanation:

`{(x = 10 (Cos t + t Sint)),(y=10 (Sint - t Cost)):}`

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

`dx/dt=10tcost`
`dy/dt=10t sint`

`(ds)/dt=10t`

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