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

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

In[1]:=

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

Out[1]=

         5
  t - 2 t

In[2]:=

  Integrate[%, {t,0,2}]

Out[2]=

    58
  -(--)
    3