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Calculus III (Notes) / Multiple Integrals / Area and Volume Revisited   [Notes] [Practice Problems] [Assignment Problems]

Calculus III - Notes
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 Area and Volume Revisited

This section is here only so we can summarize the geometric interpretations of the double and triple integrals that we saw in this chapter.  Since the purpose of this section is to summarize these formulas we aren’t going to be doing any examples in this section. 

 

We’ll first look at the area of a region.  The area of the region D is given by,

 

 

 

Now let’s give the two volume formulas.  First the volume of the region E is given by,

 

 

 

Finally, if the region E can be defined as the region under the function  and above the region D in xy-plane then,

 

 

 

Note as well that there are similar formulas for the other planes.  For instance, the volume of the region behind the function  and in front of the region D in the xz-plane is given by,

 

 

 

Likewise, the the volume of the region behind the function  and in front of the region D in the yz-plane is given by,

 

 

Surface Area Previous Section   Next Section Line Integrals (Introduction)
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals

Calculus III (Notes) / Multiple Integrals / Area and Volume Revisited    [Notes] [Practice Problems] [Assignment Problems]

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