Shania is buying a car. She has narrowed her choice down to three cars: a sedan, a hatchback, and a wagon. She uses a spinner di
vided into three colored sections to decide which car to buy. She first spins the spinner 75 times to check the frequencies that it produces. Her results are shown in the table.
2 answers:
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The Jacobian for this transformation is
with determinant , hence the area element becomes
Then the integral becomes
where is the unit circle,
so that
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
Then