Resposta:

dx/dt=3

dy/dt=3*t^(1/2)

Então:

C =de 0 a 1 ∫√[ (dx/dt)² + (dy/dt)² ] dt  

C =de 0 a 1 ∫√[ (3)² + (3*t^(1/2))² ] dt  

C =de 0 a 1 ∫√[ 9 + 9t ] dt

Substitua 9+9t =u  ==> 9dt=du

C =de 0 a 1 ∫√[u] dt/9

C= de 0 a 1 [(u^(3/2))/(3/2) ] /9

C= de 0 a 1 [(2/27)*(u^(3/2)) ]  

Como u =9+9t

C= de 0 a 1 [(2/27)*((9+9t)^(3/2)) ]  

= [(2/27)*((9+9*1)^(3/2)) ]  -  [(2/27)*((9+9*0)^(3/2)) ]  

= [(2/27)*((18)^(3/2)) ]  -  [(2/27)*((9)^(3/2)) ]  

= [(2/27)*((3√2)^(3)) ]  -  [(2/27)*(27) ]  

[(2/27)*((27√2³)) ]  -  2 ]  

(2)*(√2³)   -  2   =   4√2 -2

Letra D