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MathTrackX

Integral Calculus

Nicholas Crouch, Dr. Danny Stevenson, Dr. Brendan Harding, Dr. Melissa Humphries, and Dr. David Butler

This course is part four of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

This course will cover basic concepts and techniques relating to integration, another fundamental tool of calculus. Integration is key to understanding the accumulation of a quantity given its rate of change.

This course is part four of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will cover concepts and techniques to provide a foundation for the applications of differentiation in STEM related careers and/or further study at the undergraduate level.

Join us as we provide opportunities to develop your skills and confidence in applying mathematics to solve real world problems.

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What's inside

Learning objectives

The concept of anti-derivative as the reverse of differentiation
How to calculate the anti-derivative of polynomials and special functions

How to calculate definite integrals and their relation to areas under graphs
Applications of integration to calculating areas and solving problems in kinematics.

The concept of anti-derivative as the reverse of differentiation
How to calculate the anti-derivative of polynomials and special functions
How to calculate definite integrals and their relation to areas under graphs
Applications of integration to calculating areas and solving problems in kinematics.

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Provides a solid foundation in mathematical fundamentals and how they can be applied in the real world

Taught by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, who are recognized for their work in Mathematics

Covers concepts and techniques to provide a foundation for the applications of differentiation in STEM related careers and/or further study at the undergraduate level

Develops skills and confidence in applying mathematics to solve real world problems

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in MathTrackX: Integral Calculus with these activities:

Review Precalculus Concepts

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Strengthen your foundation by reviewing essential precalculus concepts that underpin integration.

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Revisit topics like limits, derivatives, and functions
Practice solving related problems

Gather Resources on Integration Applications

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Expand your understanding of integration's practical applications by curating a collection of resources.

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Search for articles, videos, and case studies
Organize the resources into a structured format

Read Thomas' Calculus: Early Transcendentals

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Supplement your learning with a comprehensive textbook that provides in-depth coverage of integration and its applications.

View University Calculus: Early Transcendentals,... on Amazon

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Five other activities

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Khan Academy: Introduction to Integration

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Reinforce your understanding of integration concepts with interactive video tutorials and practice exercises.

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Access the Khan Academy module
Watch the videos and complete the exercises
Seek clarification on any challenging concepts

Complete Integral Antiderivative Practice Questions

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Practice makes perfect! Sharpen your antiderivative calculation skills by completing a series of practice questions.

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Access practice question set
Attempt to solve questions independently
Review solutions and identify areas for improvement

Join a Study Group for Integration

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Collaborate with peers to solidify your grasp of integration concepts through discussions and problem-solving.

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Find or form a study group
Review concepts, solve problems, and discuss applications

Integrate Functions to Calculate Area

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Apply your understanding of integration to a practical application: calculating the area under graphs.

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Select a function to integrate
Set up the integral and evaluate
Interpret the result as the area under the graph

Contribute to the SymPy Integration Library

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Deepen your understanding of integration algorithms and their implementation by contributing to an open-source library.

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Familiarize yourself with the SymPy library
Identify potential areas for contribution
Develop and test code improvements

Career center

Learners who complete MathTrackX: Integral Calculus will develop knowledge and skills that may be useful to these careers:

Quantitative Analyst

Quantitative Analysts take a variety of data and construct models and strategies to guide investment decisions. They are employed throughout the finance industry, informing decisions for financial advisors, portfolio managers, hedge funds, and more. The models they create drive decisions to reduce risk and increase return on investment. This course is a good fit for those wishing to work as Quantitative Analysts because it provides a foundation in the application of calculus to real-world problems. This strong foundation will make it easier to learn the advanced techniques used by Quantitative Analysts.

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Business Analyst

Business Analysts use their knowledge of mathematics, statistics, and business to analyze data and make recommendations to improve business processes. They are employed in a variety of industries, including consulting, technology, and healthcare. This course may be useful for those wishing to pursue a career as a Business Analyst, as it will help you develop a foundation in integral calculus, as well as practical experience applying mathematics to solve real-world problems.

See salaries and explore the career path for Business Analyst

Operations Research Analyst

Operations Research Analysts use their knowledge of mathematics and statistics to develop and analyze models to improve decision-making. They are employed in a variety of industries, including transportation, manufacturing, and healthcare. This course may be useful for those wishing to pursue a career as an Operations Research Analyst, as it will help you develop a foundation in integral calculus, as well as practical experience applying mathematics to solve real-world problems.

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Statistician

Statisticians collect, analyze, interpret, and present data to inform decision-making in a variety of fields. The skills and knowledge you will gain in this course, including developing a foundation in integral calculus, can be applied to a variety of industries. This course can help build a solid foundation for a career as a Statistician.

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Financial Analyst

Financial Analysts use their knowledge of mathematics, statistics, and finance to analyze financial data and make recommendations to investors. They are employed in a variety of industries, including banking, investment management, and insurance. This course may be useful for those wishing to pursue a career as a Financial Analyst, as it will help you develop a foundation in integral calculus, as well as practical experience applying mathematics to solve real-world problems.

See salaries and explore the career path for Financial Analyst

Data Scientist

Data Scientists use their knowledge of mathematics, statistics, and programming to extract insights from data. They are employed in a variety of industries, including technology, finance, and healthcare. This course may be useful for those wishing to pursue a career as a Data Scientist, as it will help you develop a foundation in integral calculus, as well as practical experience applying mathematics to solve real-world problems.

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Actuary

Actuaries use their knowledge of mathematics and statistics to predict the likelihood of future events, which can be used to determine insurance rates, pensions, and more. To work as an Actuary, this course may be useful in building a foundation in integral calculus, as well as developing skills in applying mathematics to solve real-world problems.

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Software Engineer

Software Engineers design, develop, and maintain software applications. They are employed in a variety of industries, including technology, finance, and healthcare. This course may be useful for those wishing to pursue a career as a Software Engineer, as it will help you develop a foundation in integral calculus, as well as practical experience applying mathematics to solve real-world problems.

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Computer Scientist

Computer Scientists research and develop new computing technologies. They are employed in a variety of industries, including technology, finance, and healthcare. This course may be useful for those wishing to pursue a career as a Computer Scientist, as it will help you develop a foundation in integral calculus, as well as practical experience applying mathematics to solve real-world problems.

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Mathematician

Mathematicians research and develop new mathematical theories and techniques. They are employed in a variety of industries, including academia, government, and finance. This course may be useful for those wishing to pursue a career as a Mathematician, as it will help you develop a foundation in integral calculus.

See salaries and explore the career path for Mathematician

Economist

Economists use their knowledge of mathematics, statistics, and economics to analyze economic data and make recommendations to businesses and governments. They are employed in a variety of industries, including government, academia, and finance. This course may be useful for those wishing to pursue a career as an Economist, as it will help you develop a foundation in integral calculus, as well as practical experience applying mathematics to solve real-world problems.

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Physicist

Physicists use their knowledge of mathematics and physics to study the fundamental laws of nature. They are employed in a variety of industries, including academia, government, and technology. This course may be useful for those wishing to pursue a career as a Physicist, as it will help you develop a foundation in integral calculus.

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Biologist

Biologists study living organisms and their interactions with their environment. They are employed in a variety of industries, including healthcare, academia, and government. This course may be useful for those wishing to pursue a career as a Biologist, as it will help you develop a foundation in integral calculus.

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Chemist

Chemists use their knowledge of chemistry to develop new materials and products. They are employed in a variety of industries, including manufacturing, healthcare, and technology. This course may be useful for those wishing to pursue a career as a Chemist, as it will help you develop a foundation in integral calculus.

See salaries and explore the career path for Chemist

Engineer

Engineers design, develop, and maintain machines, structures, and systems. They are employed in a variety of industries, including technology, manufacturing, and healthcare. This course may be useful for those wishing to pursue a career as an Engineer, as it will help you develop a foundation in integral calculus.

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Reading list

We've selected 14 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in MathTrackX: Integral Calculus.

Numerical Methods in Mechanics of Materials

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This calculus textbook is one of the most widely used textbooks for undergraduate students. It covers the fundamentals of calculus, including integration, and provides numerous examples and practice problems.

Numerical Methods in Mechanics of Materials: With...

Paperback

$$$

Numerical Methods in Mechanics of Materials: With...

Kindle Edition

Calculus: Early Transcendentals

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Shorter version of Stewart's Calculus: Early Transcendentals, and it covers the same topics in a more concise way. It good option for students who want to learn the material in the course more quickly.

Calculus: Early Transcendentals

Paperback

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Calculus: Early Transcendentals

Kindle Edition

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Calculus

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Is specifically designed for students who are taking the AP Calculus course. It covers all of the topics that are covered on the AP exam, and it includes practice problems and review questions.

MathTrackX

Integral Calculus

What's inside

Learning objectives

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Activities

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