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12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy,...
please provide explanations. (a) (7 points) Use the Green's Theorem to evaluate the line integral y dr+ry dy, where 2 C is the positively oriented triangle with vertices (0,0), (2,0) and (2,6) (b) (7 points) Let F(x, y) = (2xsin(y) + y2) i(x2 cos(y) +2ry)j. Find the scalar function f such that Vf F. equation of the tangent plane to the surface r(u, v) (u+v)i+3u2j+ (c) (7 points) Find an (u- v) k at the point (ro, yo, 20) (2,...
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. ху 7 In(7 + y) dx - dy, where C is the triangle with vertices (0,0), (4,0), and (0,8) fe 7+ y ху f 7 ln(7 + y) dx – dy = 7+y
5. (4 points) Calculate integral $.264 + z sin y)dx + (x? cos y − 3yjº)dy along triangle with vertices (0,0), (1,0) and (1,1), oriented counterclockwise, using Green's theorem.
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. ∮C 6 ln(6+y) dx−(xy/6+y) dy, where C is the triangle with vertices (0,0), (6,0), and (0,12) ∮C 6 ln(6+y) dx−(xy/6+y)dy=
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)
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation. 9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation.
please answer all 3 questions, I need help. thank you Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(9x+ ex) dy- (4y + sinh x) dx, where C is the boundary of the square with vertices (2, 0), (5, 0), (5, 3), and (2, 3). $(9x+ ey?) ay- (4y+ + sinhx) dx = 0 (Type an exact answer.) Use Green's Theorem to evaluate the following line integral. i dy - g dx, where (19)...
Use Green's theorem to evaluate the line integral S. (sin(22) – 5y) dx + (72 – y cos y) dy, where C is the the counter clockwise oriented closed curve consisting of the upper half of the circle (x – 5)2 + (y – 4)2 = 9 and the line segment between (2, 4) and (8,4).
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)
10. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C in the xy-plane. $ 5xydx +4xdy , where C is the triangle with vertices (0,0), (5,4), and (0, 4).