Part 1
For the following parametrization $y(t) = e^{it}, t \in [0,2\pi]$ calculate the following integral
$\int_y (2z + 1)dz$
Part 2
For the following parametrization $y(t) = 1 + it, t \in [0,1]$ calculate the following integral
$\int_y (2z + 1)dz$
Part 3
We know that
F(z) = z^2 + z
F'(z) = 2z + 1
y(t) = 1 + it, t \in [0,1]
a = y(0) = 1 + i*0 = 1
b = y(1) = 1 + i*1 = 1 + i
Find
F(b) - F(a)