2. Evaluate the line integral fxydx + xºy’dy where C is the triangle with vertices с...
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).
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.
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.
(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...
Given the following vectors F=[y2, x2,x-z] and surface S: the triangle surface with vertices (0,0,1), (1,0,1), (1,1,1) in first octave. A. Evaluate the surface integral F(F) . dA B. Evaluate the surface integral VxF(F) dA C. Evaluate the line integral F() di where C is the curve enclosing the triangle. (Don't apply Green's theorem and integrate directly) Given the following vectors F=[y2, x2,x-z] and surface S: the triangle surface with vertices (0,0,1), (1,0,1), (1,1,1) in first octave. A. Evaluate the...
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
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the point (1, 0, 0) 6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the...
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)...
(a) C is the circle with center the origin and radius 1(b) (thereshould be a C under (b)'s integral sign, showing that it is a curve)C is the triangle with vertices (0,0), (1,3), and (0,3)(Only use Green's Theorem to evaluate this line integral along the given positively oriented curve)
Use Green's Theorem to evaluate the line integral along the given positively oriented curve.C is the rectangle with vertices (0,0), (5,0), (5,2), and (0,2)