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Use Green's theorem to evaluate line integral F.dr, where F(x, y) = (y2 – x2)i +...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer 4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer
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,...
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise. 12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
Evaluate the line integralho2-r)dc + (x2+y2)dy, where Cis the triangle bounded by yx3,y, by two methods: (a) directly and (b) using Green's Theorem (counterclockwise circulation) 9. Evaluate the line integralho2-r)dc + (x2+y2)dy, where Cis the triangle bounded by yx3,y, by two methods: (a) directly and (b) using Green's Theorem (counterclockwise circulation) 9.
Use Green's Theorem to evaluate the line integral ang the given positively oriented curve (3y+5eVX d(Bx5 cos(y2) dy x2 and x y2 C is the boundary of the region enclosed by the parabolas y Use Green's Theorem to evaluate the line integral ang the given positively oriented curve (3y+5eVX d(Bx5 cos(y2) dy x2 and x y2 C is the boundary of the region enclosed by the parabolas y
4.Use Green's Theorem to evaluate the line integral. ∫C 2xydx + (x + y)dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x2_______ 5.Use Green's Theorem to evaluate the line integral. ∫C ex cos(2y) dx - 2ex sin(2y) dy C: x2 + y2 = a2 _______
(a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in the counterclockwise direction n is the outward-pointing normal vector on , and C is the boundary (b) (15 points) Evaluate directly the line integral p F- nds in part (a). (a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in...
It is possible to use Green's Theorem to calculate the path integral S.F.ds, where F(x, y) = (-y/(x2 + y²), x/(x2 + y2)) and c is the unit circle x2 + y2 = 1, oriented positively.
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...