1 (4 points). Find the work done when the force F(x,y) = x^2 i - y j acts on an object moving along the curve x[t] = t, y[t] = t^2, from (0,0) to (3,9).

Solution: x'[t] = 1 and y'[t] = 2 t. The integral is the integral with respect
to t of (x[t])^2 x'[t] - y[t] 2 t

In[3]:=

  x[t_] := t
  y[t_] := t^2
  x[t]^2 x'[t] - y[t] (y'[t])

Out[3]=

   2      3
  t  - 2 t

In[4]:=

  Integrate[%, {t,0,3}]

Out[4]=

    63
  -(--)
    2