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,...
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...
8. Evaluate $c (4xy3 + 3y) dx + (8x – 6x?y?) dy where C is the triangle formed by vertices (0, 0), (3,0), (3, 4) 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...
Problem 8. Evaluate Jo y' dz + 3zy dy, where C is the boundary of the semianmulan region D in the upper half-plane between the circles x2 + y2 = 1 and x2 + y-4. ANSWERS. Problem 8. Evaluate Jo y' dz + 3zy dy, where C is the boundary of the semianmulan region D in the upper half-plane between the circles x2 + y2 = 1 and x2 + y-4. ANSWERS.
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...