Trigonometry | Complex Numbers | Geometric Series | Integrals of Complex Functions and Integration by parts |

In this class, we will deal only with integrals of complex functions of a real variable integrated with respected to the real variable. This is identical to integration of real functions of real variables. The $j$ is simply treated as a constant in all these cases. In this class, we are typically interested in time $t$ or frequency $\omega$ being the independent variable. Hence, the integrals will be with respect to $t$ or $\omega$.

For example,

$\int_0^{\pi/4} e^{j 2 t} \ dt = \left[\frac{e^{j 2 t}}{2 j}\right]_{0}^{\pi/4} = \frac{j-1}{2j}$

Sometimes we will have to use Integration by parts to evaluate integrals. The main result to recall is

(1)**Example:**

Evaluate $\displaystyle{\int_0^1 t e^{-j \omega t} dt}$, where $\omega$ is any complex number

We choose