Question

Use Green's Theorem to evaluate the line integral along the given positively oriented curve.

C |

9*y*^{3}* dx* −
9

*C* is the circle *x*^{2} +
*y*^{2} = 4

Answer #1

Use Green's Theorem to evaluate the line integral along the
given positively oriented curve.
C
3y + 7e
x
dx +
8x + 3 cos(y2)
dy
C is the boundary of the region enclosed by the
parabolas
y = x2 and x = y2

Use Green's Theorem to evaluate the line integral along the
given positively oriented curve.
C
3y + 7e
x
dx +
8x + 9 cos(y2)
dy
C is the boundary of the region enclosed by the
parabolas
y = x2 and x = y2

Use Green's Theorem to evaluate the line integral along the
given positively oriented curve. C 3y + 5e x dx + 10x + 9 cos(y2)
dy C is the boundary of the region enclosed by the parabolas y = x2
and x = y2

Use Green's Theorem to evaluate the line integral
∫CF·dr
along the given positively oriented curve.
F(x, y) = ‹
x2e-2x,
x4 +
2x2y2 ›
C is the boundary of the region between the circles
x2 + y2 = 1 and
x2 + y2 = 25 in the
4th quadrant.

Use Green's Theorem to evaluate the line integral along the
given positively oriented curve.
∫ F dx where F(x,y) =-yx^2i + xy^2j
(lower bounds C)
C consists of the circle x^2 + y^2 = 16 from (0,4) to(2√2,
2√2)and the line segments from (2√2, 2√2) to (0, 0) and from (0, 0)
to (0,4)

Use Green's Theorem to evaluate the line integral.
C
(x2 −
y2) dx +
5y2dy
C: x2 +
y2 = 4

Let C be the positively oriented square with vertices (0,0),
(2,0), (2,2), (0,2). Use Green's Theorem to evaluate the line
integral ∫C3y2xdx+3x2ydy.

Evaluate the line integral of
(x2+y2)dx + (5xy)dy over
the border of circle x2+y2=4 using Green's
Theorem.

Use Stokes' Theorem to evaluate
C
F · dr
where C is oriented counterclockwise as viewed from
above.
F(x, y,
z) = yzi +
6xzj +
exyk,
C is the circle
x2 +
y2 = 9, z = 2.

Use Green’s Theorem to evaluate the integral H C x ln ydx where
C is the positively oriented boundary curve of the region bounded
by x = 1, x = 2, y = e^x and y = e^(x^2) .

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