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is the Use Stokes' theorem to evaluate ſc(1+y)z dx + (1+z)x dy+(1 + x)y dz, where counterclockwise-oriented triangle with vertices (1,0,0), (0,1,0), and (0,0,1).
7. Evaluate (6x - 6y+8) dx+(4 +9y +7) dy where C is the boundary of the triangle in the ry plane, wit h vertices at (0,0), (1,0)and (1,4) traversed once anticlockwise. (a) 10 (c) 20 (b)-8 (d) 8 10. Find the flux of F =-rit 2yj otward across the ellipse-+ -1. (a) 36π (b) 18m (c) o (d) 6π 7. Evaluate (6x - 6y+8) dx+(4 +9y +7) dy where C is the boundary of the triangle in the ry plane,...
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3) 5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
Evaluate ∫C(2x - y) dx + (x + 3y)dy C: arc on y=x5/2 from (0, 0) to (4, 32) _______
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.
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...
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)
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=
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.
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