Evaluate the integral c xy ds where C is the curve parametri

Evaluate the integral c xy ds where C is the curve parametrized by x = t2, y = t -2 and 1

Solution

dx= 2t dt ;
dy = -2t^-3 dt;

so

₀² ₀² t².t^-2 . 2tdt * - 2t^-3 dt ;

₀² ₀² -4t^-2 dt dt ;

so evaluating we get 4 log (2) ;