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Applications of the change of variables theorem : Integration over triangular and square regions and changing an integral from rectangular to polar coordinates.

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(1) Find ...
(x + y)2 dx dy...where R is the square with vertices (±1, 0) and (0,±1),

(2) Let R now be the triangular region in the xy plane with vertices (1, 0), (2, 1), (3, 0).
Find....

(3) Change the integral
....
from rectangular to polar coordinates.

See the attached file.

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Applications of the change of variables theorem, integration over triangular and square regions and changing an integral from rectangular to polar coordinates are investigated. The solution is detailed and well presented.

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