10.26 - Section 12.2: Double integrals over general regions...

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Section 12.2: Double integrals over general regions Main ideas? ..?. . Extending from rectangles to general bounded regions (“hitching a ride” on what we did before) Regions of Type I and Type II, and iterated integrals of the form a b f ( x ) g ( x ) F ( x , y ) dy dx and c d h ( y ) k ( y ) F ( x , y ) dx dy Changing order of integration Algebraic properties of the double integral (revisited) Let D be an irregular domain, living inside a rectangle R . Why do we bother with the fuss of defining ( f ( x , y ) if ( x , y ) in D , F ( x , y ) = ( ( 0 otherwise instead of “just integrating over D ”? ..?. . We haven’t defined yet what it means to integrate over a non-rectangular region! Let D be the triangular region bounded by the lines x = 0, y = x /2, and y = 1.
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Sketch D . ..?. . It’s the triangle with vertices (0,0), (0,1), and (2,1). Is D of Type I, Type II, or both? ..?. . Both.
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10.26 - Section 12.2: Double integrals over general regions...

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