AI - Applications of Integration Module Overview

Applications of Integration Module Overview

Introduction

Applications of Integration wordleIntegral calculus is renowned for the solutions it provides to an enormous number of problems, both mathematical and applied. In many practical applications a definite integral is used to measure something such as area, volume, length of a curve, and a physical or economic quantity. The hardest part is identifying the appropriate integral that measures the given quantity. Often times a pattern to defining and calculating integrals in application settings emerges and paves the way for defining new integrals that fit particular situations.

Essential Questions

  • What information is needed before using integrals to find areas of complex figures?
  • How can integrals be used to find volumes of solids of revolution?
  • How is the arc length of a curve on a given interval computed?
  • What are some practical applications of finding areas, volumes, and arch length? 

Key Terms

The following key terms will help you understand the content in this module.

Area between two curves - The planar region formed by the boundaries of two or more continuous curves over a given interval.

Axis of revolution - The line about which a planar region is revolved.

Cross section - A plane region formed by slicing (cutting) through an object at an angle perpendicular to its axis.

Disk method - A technique for computing volume of a solid using cross sections perpendicular to the axis of revolution. The revolved region borders on the axis of revolution.

Shell method - A technique for computing volume using cross sections parallel to the axis of revolution.

Solid of revolution - Solid formed by revolving a region in the xy-plane about an axis.

Volume of a solid of revolution - The amount of space occupied by a planar region that has been revolved about an axis.

Washer method - A technique for computing the volume of a region not bordering on the axis of revolution that uses cross sections perpendicular to the axis of revolution. The resulting solid has the shape of a washer with an outer radius and an inner radius.

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