Soumik has $5 less than his friend Kofi. If they have $97.50 altogether, how much does each
2 answers:
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Check the picture below.
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