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General formula for Area Problems:
The area between and which are two non-intersected curves is given by:
The Disk Method:
The disk method is the method to calculate the volume of a solid revolution through slicing the solid perpendicular to the axes and integrating the volume of each slide along axis of the solid.
The Washer Method:
The washer method is the method to calculate the volume of a hollow solid revolution through slicing the solid perpendicular to the axis and integrating the volume of each slide along axis of the solid.
The Shell Method:
The shell method is the method to calculate the volume of a solid revolution through cutting the shell-type solid through the radius direction and accumulating the shell-type cuts along the radius direction.
Rapid Study Kit for "Title":
Core Concept Tutorial
Problem Solving Drill
Review Cheat Sheet
"Title" Tutorial Summary :
The use of integration is used to find the area and volume of solids. Graphical representation of the areas and volumes of solids is represented with the help of examples. The idea behind the area between two curves is mentioned in this tutorial. Formulas for the areas enclosed by two curves are shown with the use of graphical examples.
Area and volume problems are presented with the assistance of examples and theorems. The integral is presented as a series of a generalization of area, mass, volume, sum and total. Volume problems are treated using disk, washer and shell methods. The methods to find the volumes of solids are compared with each other.
Specific Tutorial Features:
Graphical illustration of the integration methods to find the area of solids.
Graphical illustration of the integration methods to find the volume of solids.
Examples showing the differences between the washer, disk and shell method.
Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
Definition slides introduce terms as they are needed.
Visual representation of concepts
Animated examples—worked out step by step
A concise summary is given at the conclusion of the tutorial.
"Title" Topic List: