Evaluate the given integral by changing to polar coordinates.
10. , where R is the region that lies between the circles x2 + y2 = a2 and x2 + y2 = b2 with 0 < a < b
To evaluate: The given integral by changing into the polar coordinates.
The function, .
The region R lies between the circles centered at origin and the radii a and b, respectively with 0 < a < b.
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 R, it is observed that the value of r varies from a to b and the value of varies from 0 to Substitute and .
Therefore, by the equation (1) the given integral becomes,
Integrate the function with respect to and r by using the equation (2)
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