Evaluate the iterated integral by converting to polar coordinates

polar-coordinates

#1

Evaluate the iterated integral by converting to polar coordinates.

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Answer:

Consider the following iterated integral:
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That is, the region is the top half of the disk centered at (O, 1) with radius 1.
The polar coordinates for region R is
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The region of in tegration in polar coordinates as,
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Therefore, the given integral becomes,
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Hence the above integral becomes,
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