Complex Analysis: Applications of Cauchy-Goursat Theorem

In this integral worksheet, pupils compute definite integrals, sketch line segments and shade regions for the integrals. This one-page worksheet contains six multi-step problems.

Use the Fundamental Theorem, not just look at it. Learners watch as the video walks viewers through finding the definite integral of a trigonometric function. The presenter provides helpful suggestions as she evaluates the example...

How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to evaluate a definite...

Integrate a great resource into your lesson plans. The eighth video in an 11-part series explains integration and the relationship between derivatives and integrals. The relationship between a car's velocity and its travel distance helps...

Demonstrate a complex integration by using partial fractions with an AP Calculus resource that works an example of integrating a rational function. The function's denominator has linear factors with one of them repeated. 

What are the properties that can be associated with the definite integral? The AP Calculus video lists nine properties of the definite integral and provides explanations of why the properties hold for integrals in language that is simple...

The concept of solving integrals by substitution with trigonometric functions is modeled by a video designed for AP Calculus classes. The narrator works an example problem using substitution and shows that careful substitution makes...

Class members view how to derive the formula to integrate by parts with a video that uses the Product Rule from the beginning of AP Calculus to derive the rule to integrate products. The resource shows the formula in two different forms,...

Present examples of trigonometric integrals with a video that shows an example of determining a trigonometric integral. The AP Calculus example shows that many of the trigonometric integrals require manipulation and using trigonometric...

The nth roots of unity all have a magnitude of one. Scholars use the unit circle and DeMoivre's Theorem to find the complex roots of one and discover that the complex numbers all lie on the unit circle and are equally spaced around it...