For 1 the equation of the parabola is y = x^2 - 8x + 3
For 2 the equation of the parabola is y = -2x^2 - 3x + 1
For 3 the equation of the parabola is y = -x^2 + 5x - 4
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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
Answer:
Jim - Ocean, because lakes don't have waves to surf on. Oceans do.
Darrell - Lake, because it's the only other water option.
Janet - Mountains, because Stephanie doesn't live in the mountains.
Stephanie - Desert, because it's the only one left.
Hope I could help!
~ Marshy ~
Same girl oh my god it won’t let me ask anymore questions. Not my fault my math teacher gave me 30 questions to ask
