Question

Evaluate the line integral by the two following methods.

xy dx + x^{2}y^{3} dy

*C* is counterclockwise around the triangle with vertices
(0, 0), (1, 0), and (1, 2)

(a) directly

(b) using Green's Theorem

Answer #1

please like my solution

Evaluate the line integral by the two following methods.
(xy dx + x2 dy)
C is counterclockwise around the rectangle with
vertices (0, 0), (2, 0), (2, 1), (0, 1)
(a) directly
(b) using Green's Theorem

Evaluate the line integral:
(x^2 + y^2) dx + (5xy) dy on the edge of the circle: x^2 + y^2 = 4.
USING GREEN'S THEOREM.

Use Green’s theorem to evaluate the integral: ∫(-x^2y)dx
+(xy^2)dy where C is the boundary of the region enclosed by y=
sqrt(9 − x^2) and the x-axis, traversed in the counterclockwise
direction.

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

Evaluate the line integral of " (y^2)dx +
(x^2)dy " over the closed curve C which is the triangle
bounded by x = 0, x+y = 1, y = 0.

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

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 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)

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