(906, #13) Evaluate the line integral:

where C: x = 2 t, y = t2, z = t2, t = 0..1

Solution: On C

x = 2 t
y = t2
z = t2
t = 0..1
x3 y2 z =8 t3+4+2 = 8 t9

Note that we are integrating with respect to z, so

dz = 2 dt.

Consequently,


by C.A.H.