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MA 242.003 . Day 33 – February 21, 2013 Section 12.2: Review Fubini’s Theorem Section 12.3: Double Integrals over General Regions. Compute the volume below z = f(x,y ) and above the rectangle R = [ a,b ] x [ c,d ]. To be able to compute double integrals we need the concept

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Ma 242 003
MA 242.003

  • Day 33 – February 21, 2013

  • Section 12.2: Review Fubini’s Theorem

  • Section 12.3: Double Integrals over General Regions


Ma 242 003

Compute the volume below z = f(x,y) and above the rectangle R = [a,b] x [c,d]




Ma 242 003

Section 12.3: Double Integrals over General Regions

“General Region” means a connected 2-dimensional region in a plane bounded by a piecewise smooth curve.


Ma 242 003

Section 12.3: Double Integrals over General Regions

“General Region” means a connected 2-dimensional region in a plane bounded by a piecewise smooth curve.


Ma 242 003

Section 12.3: Double Integrals over General Regions

Problem: Compute the double integral of f(x,y) over the region D shown in the diagram.


Ma 242 003

Section 12.3: Double Integrals over General Regions

Problem: Compute the double integral of f(x,y) over the region D shown in the diagram.

Solution:


Ma 242 003

Section 12.3: Double Integrals over General Regions

Problem: Compute the double integral of f(x,y) over the region D shown in the diagram.

Solution:


Ma 242 003

Section 12.3: Double Integrals over General Regions

Problem: Compute the double integral of f(x,y) over the region D shown in the diagram.


Ma 242 003

Section 12.3: Double Integrals over General Regions

Problem: Compute the double integral of f(x,y) over the region D shown in the diagram.

It turns out that if we can integrate over 2 special types of regions,


Ma 242 003

Section 12.3: Double Integrals over General Regions

Problem: Compute the double integral of f(x,y) over the region D shown in the diagram.

It turns out that if we can integrate over 2 special types of regions, then properties of integrals implies we can integrate over general regions.





Ma 242 003

Question: How do we evaluate a double integral over a type I region?


Ma 242 003

Question: How do we evaluate a double integral over a type I region?


Ma 242 003

Question: How do we evaluate a double integral over a type I region?


Ma 242 003

Question: How do we evaluate a double integral over a type I region?







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