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Example Questions
Example Question #1 : Double Integration In Polar Coordinates
Evaluate the following integral by converting into Polar Coordinates.
, where
is the portion between the circles of radius
and
and lies in first quadrant.
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Explanation:
We have to remember how to convert cartesian coordinates into polar coordinates.
Lets write the ranges of our variables and
.
Now lets setup our double integral, don't forgot the extra .
Example Question #2 : Double Integration In Polar Coordinates
Evaluate the integral
where D is the region above the x-axis and within a circle centered at the origin of radius 2.
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Correct answer:
Explanation:
The conversions for Cartesian into polar coordinates is:
The condition that the region is above the x-axis says:
And the condition that the region is within a circle of radius two says:
With these conditions and conversions, the integral becomes:
Example Question #3 : Double Integration In Polar Coordinates
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Example Question #4 : Double Integration In Polar Coordinates
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Example Question #5 : Double Integration In Polar Coordinates
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Example Question #6 : Double Integration In Polar Coordinates
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Example Question #7 : Double Integration In Polar Coordinates
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Example Question #8 : Double Integration In Polar Coordinates
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Example Question #9 : Double Integration In Polar Coordinates
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Example Question #10 : Double Integration In Polar Coordinates
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