Problem Set 29, Due
(1) Suppose that
∂Q
∂x =∂P
∂y + 2
and the simple closed positively oriented curve Cencloses a region Dof
area 3. Compute
ZC
< P, Q > ·dR.
(2) Consider positively oriented curve E(t) =<4 cos(t),5 sin(t)>,t∈[0,2π].
Trace this curve. What region does it enclose? Now suppose that
∂Q
∂x =∂P
∂y +x
Compute
ZC
< P, Q > ·dR.
(3) Suppose that the positively oriented simple closed curve Cencloses a region
Dwhose moment of inertia around the origin is I. If
∂Q
∂x −∂P
∂y = 2x2+ 2y2
then what is ZC
< P, Q > ·dR?
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