Integral Calculus

Course Number:

MTH 252Z

Transcript Title:

Integral Calculus

Created:

Aug 15, 2022

Updated:

May 31, 2025

Total Credits:

4

Lecture Hours:

30

Lecture / Lab Hours:

20

Lab Hours:

0

Satisfies Cultural Literacy requirement:

No

Satisfies General Education requirement:

Yes

Grading Options

A-F, P/NP, Audit

Default Grading Options

A-F

Repeats available for credit:

0

Alignment with Institutional Learning Outcomes

Major

1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)

Major

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

Major

3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy)

Not Addressed

4. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)

Not Addressed

5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Institutional Learning Outcomes (ILOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

Major Designation

1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Minor Designation

1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Suggested Outcome Assessment Strategies

The determination of assessment strategies is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: writings (journals, self-reflections, pre writing exercises, essays), quizzes, tests, midterm and final exams, group projects, presentations (in person, videos, etc), self-assessments, experimentations, lab reports, peer critiques, responses (to texts, podcasts, videos, films, etc), student generated questions, Escape Room, interviews, and/or portfolios.

Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

The grade will include at least one project.

Course Content

Outcome #1: Approximate definite integrals using Riemann sums and apply this to the concept of accumulation and the definition of the definite integral.

• Areas and Distances

• Riemann Sums

• The Definite Integral

Outcome #2: Explain and use both parts of the Fundamental Theorem of Calculus.

• The Fundamental Theorem of Calculus

• Part One - Definite Integral is Anti-derivative

• Part Two - Evaluation property of definite integrals

Outcome #3: Choose and apply integration techniques including substitution, integration by parts, basic partial fraction decomposition, and numerical techniques to integrate combinations of power, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions.

• The Substitution Rule

• Integration by Parts

• Partial Fractions

• Trigonometric Integration (of lesser importance)

• Trigonometric Substitution (of lesser importance)

• Numerical Integration

  • Midpoint Rule

  • Trapezoid Rule

  • Simplson’s Method

Outcome #4: Use the integral to model and solve problems in mathematics involving area, volume, net change, average value, and improper integration.

• More About Areas

• Volumes

• Volumes by Slicing

  • Rotation about the independent variable

• Volumes by Cylindrical Shells

• Arc Length

• Average Value of Functions

  • Mean Value Theorem for Integrals

• Improper Integration 

Outcome #5: Apply integration techniques to solve a variety of problems, such as work, force, center of mass, or probability.

• Work

  • Hooke’s Law

  • Other applications involving either variable force or distance

• Force of Fluids

• Center of Mass/Centroids

• Applications to Economics and Biology

  • Consumer/Supplier Surplus

  • Poiseuille’s Law

• Probability

• Separable Differential Equations

  • Continuous Growth

  • Logistics Model

Suggested Texts and Materials

Calculus, Vol. 2 Openstax, Strang, Herman
This is an open textbook available at: https://openstax.org/details/books/calculus-volume-2

A graphing utility is required. We use Desmos; it is available as a free app for smartphones and tablets (from the app store) or through a browser on a laptop or desktop computer at: https://www.desmos.com

Department Notes

Answers to all application problems will be given in complete sentences with correct units. The grade will include at least one project.