Calculus: Single Variable Part 4 - Applications

Penn applies single-variable calculus to geometry, physical quantities and probability. Areas and volumes lead into other geometric and physical applications, followed by averages and mass. The course gives learners several ways to interpret an integral, which can be useful after a sequence focused mainly on calculating antiderivatives.

What you will learn

• Use integrals to describe areas and volumes.
• Relate calculus to averages and mass.
• Explain an introductory connection between integration and probability.

Who this suits

Coursera labels the course mixed level. Preview earlier integration material and the setup of applied problems before enrolling.

Before you enroll

Work through the algebra as well as the numerical answer. Sketch the function or region involved and check which assumptions allow the chosen calculus method to apply.

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Put it into practice

Set up an integral for a fictional density that varies along a rod. Explain the units and why an ordinary average may be inappropriate.

Source and review

This overview is based on the provider's published information, checked on 12 October 2026. It is an editorial assessment, not a claim that we completed the resource. Time filters are approximate study ranges; projects and exercises can take longer.

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