The statement of Green's theorem is:
Now let's begin to solve given question as:
Note: for any query or explanation in any step kindly mention it in the comment section. I will assist you as soon as possible.
Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40 Problem...
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where C is the triangle with vertices (0,0), (1,0) y (1,2)
...HELPPPP....Use Green’s theorem to evaluate Z C (−y + √3 x 2 )dx + (x 3 − ln (y 2 ))dy where C is the rectangle with vertices (0, 0), (1, 0), (0, 2), and (1, 2). 4. Use Green's theorem to evaluate vertices (0,0), (1,0), (0, 2), and (1,2). Sc(-y + V 22)dx + (z? – In (y?))dy where C is the rectangle with
Use Green's Theorem to calculate the line integral f. 2xy dx + 2(x+y) dy, where C is the unit circle centered at the origin and it is counter-clockwise oriented. $c 2xy dx + 2(x + y) dy =
Use Green's Theorem to evaluate the line integral 2xy dx + (2x + y) dy с where C is the circle centered at the origin with radius 1. Start by sketching the region of integration, D.
(1 point) Use Green's theorem to evaluate where C is the rectangle with vertices (0,0). (3,0) (3,2) and (0, 2) O A. I- 12 B. 1-24 O C. I- 48 E. I96 (1 point) Use Green's theorem to evaluate where C is the rectangle with vertices (0,0). (3,0) (3,2) and (0, 2) O A. I- 12 B. 1-24 O C. I- 48 E. I96
2. (8 pts) Use Green's Theorem to evaluate fcln(1 + y) dx - triangle with vertices (0,0), (2,0) and (0,4). 17, dy, where C is the
Use Green's theorem to evaluate the line integral Sc xay dx + 2xy?dx where C is the triangle with vertices 10,0), 12, 2), and 12,8).
Problem. Use Green's Theorem, to evaluate the line integral, 5. Pdr + Qdy = 1] (e. - SP) da, 1. (=x+ + e* In y)dx + (x + y + ) dy, where C is the triangle with the vertices (1,1), (2.1), and (2, 2), and the positive (counter- clockwise) orientation. (10 points)
5) Use Green's Theorem to evaluate | (xy)dx + (y2 +4)dy where is the cardoid r = 1 + sine OSOS 21 с
Evaluate the following integrals using Green's theorem. 8. S. (2y2 + xsin(x)dx + (x3 - evy)dy where c is the rectangle in R2 with vertices at (1,0), (2,0), (2,2) and (1,2) oriented counterclockwise.