Jonas Reitz | D744 | Fall 2024

Category: Resources

Classwork: The Definite Integral and the Fundamental Theorem of Calculus

Definition: The Definite Integral.

If $f(x)$ is a function defined on an interval $[a, b]$, the definite integral of $f$ from $a$ to $b$ is given by

$$
\int_a^b f(x) d x=\lim {n \rightarrow \infty} \sum_{i=1}^n f\left(x_i^*\right) \Delta x
$$

provided the limit exists. If this limit exists, the function $f(x)$ is said to be integrable on $[a, b]$, or is an integrable function.

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Course Hub

Go to the MAT 1575 Course Hub

About the MAT 1575 Course Hub

The Course Hub is a central resource created by the Mathematics Department for information and resources related to MAT 1575 Calculus II. Whether you are a student in the course or a faculty member teaching it, we hope you will find useful material there. Some of the resources you will find include:

  • Online Lessons. Here you will find (optional) online lessons for each day of class. If you missed a day of class, or you have questions, this is a great place to go!
  • WeBWorK Resources for Students and Faculty. Need help with WeBWorK? Whether you are a student stuck on a problem in the homework, or a faculty member trying to create a quiz, there are resources to help.
  • Video Resources. Stuck on a topic? Already looked at the online lesson? You can find additional videos for most topics here, including many examples worked out in full, created or selected by City Tech faculty.
  • Faculty Training and Support. Includes more general (non-WeBWorK) topics like: How do I create a discussion board in my course? How do I collect student work using DropBox? Etc.

Go to the MAT 1575 Course Hub