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Conservative Vector Field, Potential Function, Green’s Theorem, Oriented Counterclockwise, Mass Density Function, Compute Mass, Center of Mass, Order of Integration, Calculate Integral, Values of Function. Above given points are from questions of this past exam paper. Its past exam paper of Calculus III.
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MA-227, Calculus III Common Final Test April 29, 2011
Time available: 150 min Each problem is 10 points Print your name:
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F^ ~ (x, y) = (ey^ − y sin x)~i + (xey^ + cos x)~j
is a conservative vector field, and if yes, find a potential function f for it.
C F~ · d~r, where
F^ ~ (x, y) = 〈sin x − 3 x^2 y, cos y + 3xy^2 〉,
and C is the circle x^2 + y^2 = 4 oriented counterclockwise.
∫ (^16)
0
y^1 /^4
ex
5 dxdy.
F^ ~ (x, y) = x^5 /^2 ~i + x√y~j.
