Question

Problem 3 The curve C is given by the parameterization r(t) = (t?,t) for 0 <t< 1. Find the midpoint of this curve.

Answer 1

1P16-1) Curve C is given by r(t) = ( t t for length of the curve oztat o t - Here, a=t, yať la fel de 7 + (d.ge at 2 2 2 2 2 2 9 ya O = S, Peter y de to Jo VQ+)+(343) dt - upper part only will be th curve = 'vert +9+" dt = ft J4+98 dt on let 9+9+² = ? ,: 18+dt db 1 ++dt - if t=0 then p=4 is t=1 then b=13 % to to loo the to Tl = 7(1378) 1.43971

[P16-2] At the mud point length of the curre will be hay the length of total curve from 4=0 to t =1 let the key mid point ocurs at to -Svetat en la at = st V@'+ (20)? dt That'+94" = ffV4+9+ dt let 4+9+ =p : 18+4+=db at t-o ,b=4 at t=top =4+9 to :!.9 (1398) = (6 +943798) Ligh - 4 = (4+9+2)348 → † Ito = 0.75253] .: Mid point will be to, ta) - (0.5663,0.4262)