(906, #3) Evaluate the line integral

where C is the right half of the circle x2 + y2 = 16.

Solution:

The parametrization of this half-circle is

x = 4 cos(t),
u = 4 sin(t),
t = -Pi/2 .. Pi/2

In addition,

ds = sqrt( (-4 sin(t))2 + (4 cos(t))2 ) ) dt = 4 dt

Consequently