Evaluate the iterated integral by converting to polar coordinates.
To evaluate: The iterated integral using polar coordinates.
The function is, .
The variable x varies from 0 to and y varies from to .
If is a polar rectangle R given by where , then, (1)
If is the function of and is the function of then,
In order to convert the given function into polar coordinates, substitute . Thus, z becomes,
Moreover, from the given condition of x and y, the value of r varies from 0 to 1 and the value of varies from 0 to .
Therefore, by the equation (1), the value of the iterated integral becomes,
Integrate the function with respect to r and by using the equation (2)
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