9.) (12 pts.) Let loop C be the triangle with vertices (0,0), (2,0), and (2,6). Evaluate...
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
(b) Evaluate the double integral e(y-2)/(y+2) dA where D is the triangle with vertices (0,0), (2,0) and (0,2). (Hint: Change variables, let u = y - x and v = y + x.)
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.
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)...
Q1. Let C be the boundary of the finite region joining the points (0,0), (2,0) and (0,1). Compute the line integral $ 2xy dx. (a) Directly (b) Using Green's theorem
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
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)
Problem #3: Use Green's Theorem to evaluate the following integral er dx + (3x + 9) dy Where C is the triangle with vertices (0,0), (12,0), and (6,8) (in the positive direction).