Find the line integral

                                     /
                                    |   ->  ->
                                    |   F * dr
                                    |
                                   /
                                     C

F = <y,x^2>
and
C is given by
x = t^3
y = 2 + t
0 <= t <= 1

Answer

 /
|   ->  ->
|   F * dr =
|
/
 C

   1
  /
 |                              81
 | <2+t, (t^3)^2><3t^2, 1> dt = --
 |                              28
/
 t=0

<2+t,(t^3)^2><3t^2,1> = 6t^2 + 3t^3 + t^6

                       1
                      |
  (2t^3+3t^4/4+t^7/7) | = 2+3/4+1/7 = 56/28+21/28+4/28 = 81/28
                      |
                       t=0