# Ch 16: Applications of Integrals

Work through these lessons on real-world applications of integrals to get a handle on calculating area, volume, and arc length using integrals. Test your skills using the lessons quizzes and chapter test.

## Applications of Integrals - Chapter Summary and Learning Objectives

We all memorized equations such as A = 1/2 base x height, A = ? x r^2, and V=base x height x length in basic arithmetic classes, but those and other area equations, simple and complex, are derived from working with integrals in calculus. Explore area and volume in more complicated shapes in this chapter on using integrals in our everyday life. The video lessons are brief and full of expert instruction you're unlikely to forget. Use the quizzes and chapter test to gauge understanding and figure out which topics you may want to revisit for further practice. In this chapter you will discover more about:

• Dynamic motion and integration
• Calculating simple areas with roots and integration
• Finding the area between functions
• Determining volumes with single integrals
• Calculating volumes of revolution through integration
• Determining a function's arc length

Video Objective
Integration and Dynamic Motion This video describes how to determine position or velocity at a given point using integration of a function f(x) wherein position is a function of time.
How to find Simple Areas With Root Finding and Integration Learn to use the root of an equation to determine the area of a space created within the intersections of several functions in this lesson.
How to Find Area Between Functions with Integration Instructors describe how to use integration to find areas with complex boundaries.
How to Calculate Volumes Using Single Integrals This video explores how the concept behind Riemann sums can be used to 'slice' an object and find the sum of the slices.
How to Find Volumes of Revolution With Integration Do some more slicing as you learn how to find volumes of objects which are symmetrical along an axis in this video.
How to Find the Arc Length of a Function In this video our instructors explain how to calculate the distance between two points when the path is an arc rather than a straight line.

6 Lessons in Chapter 16: Applications of Integrals
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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