Activity 1
Consider the points
 and
 .
Evaluate the integral from A to B
a) along the parabola
b)
along the line segment from A to
 and
then along the line segment from C to B
c)
along the line segment from A to B.
Activity 2
Consider the points A(0,0) corresponding to
the number z=0 and B(4,2) corresponding to
the number z=4+2i. Evaluate the integral from A
to B
a)
along the line segment from A(0,0) to the point
C(0,2) corresponding to z=2i and then along the
line segment from C to B.
b)
along the line segment from A to B.
c)
What do you observe?
Activity 3
Consider the points A(0,0) corresponding to
the number z=0 and B(4,2) corresponding to
the number z=4+2i. Evaluate the integral from A
to B
a)
along the line segment from A(0,0) to the point
C(0,2) corresponding to z=2i and then along the
line segment from C to B.
b)
along the line segment from A to B.
c)
What do you observe in connection with the Fundamental
Theorem of Calculus for a complex variable? |
