Evaluate the given integral by changing to polar coordinates.
14. where D is the region in the first quadrant that lies between the circles x2 + y2 = 4 and x2 + y2 = 2x
To evaluate: The given integral by changing into the polar coordinates.
The function, .
The region D is lies between the circles and in the first quadrant.
If is a polar rectangle R given by where , then, (1)
If is the function of and is the function of then,
From the given region D, it is observed that the value of r varies from 0 to 2 and the value of varies from 0 to . The region D lies between the two given curves.
Substitute and in the equation (1),
Integrate the function with respect to and r by using the equation (2).
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