Let C be the positively oriented circle . Use Green's Theorem to
evaluate the line integral .

6.2832

The work

2.

Let C be the positively oriented square with vertices ( 0, 0 ), ( 3, 0 ), ( 3, 3 ), ( 0, 3 ). Use
Green's Theorem to evaluate the line integral .

243

The work

3.

A)
Use Green's theorem to compute the area inside the ellipse
.
Use the fact that the area can be written as
Hint: .
The area is .

B)
Find a parametrization of the curve and use it to compute
the area of the interior.
Hint: .

A) 263.89

B) 57.73

The work

4.

Use Green's theorem to compute the area inside the ellipse
.
That is use the fact that the area can be written as
for appropriately chosen P and Q.
The area is .

47.124

The work

5.

Use Green's theorem to compute the area of one petal of the
36-leafed rose defined by r = 7sin(18&theta).
It may be useful for recall that the area of a region D enclosed by a
curve C can be expressed as .