Question Help LetF=v(xy?) and let C be the path in the xy-plane from (-44) to (4.4)...
11. LetF(x, y) - (2xe), x + x-e)) and let C be the quarter-circle path from A to B in Figure 18. Evaluate 1-φ F . dr as follows: (a) Find a function f (x, y) such that F- G + V f, where G (0, x). (b) Show that the line integrals of G along the segments OA and OB are zero. (c) Evaluate I. Hint: Use Green's Theorem to show that B (0,4) A (4, 0) FIGURE 18
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)
7. (10 points) Consider the linear path "C" in the xy-plane from the point (1,1) to the point (2,3). (a) Find an appropriate vector valued function r(t) along with an appropriate interval a <t<b which describes the path C. (b) Evaluate the line integral 2xy ds where C is the curve you found above.
let F(x,y) = 3x^2y^2i+2x^3yj and c be the path consisting of
line segments from(1,2) to (-1,3), from (-1,3) to (-1,1), and from
(-1,1) to (2,1). evaluate the line integral of F along c.
Let F(x, y) = 3x²y2 i + 2x’yj and C be the path consisting of line segments from (1, 2) to (-1,3), from (-1, 3) to (-1, 1), and from (-1, 1) to (2, 1). Evaluate the line integral of F along C.
(1 point) If C is the line segment from (7,4) to, (0,0), find the value of the line integral: Sc(3y2 7 + 2x1).dñ = ī (1 point) Find Sc((x2 + 3y)i + 5y37) . • dr where C consists of the three line segments from (1,0,0) to (1,1,0) to (0,1,0) to (0,1, 3). Sc((x2 + 3y)ī + 5y37). . dr =
F.df, where F(x, y, z) = (yz, uz, xy), and C is ANY smooth path from (0,0,0) to 11. a) Evaluate (2, -1, -2). b) If a particle sat at (0,0,0), give a possible physical interpretation of the line integral you com puted.
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify your answer. iii. Find a function y: R3-+ R such that F iv. Evaluate F.dr where「is the path y =r', z = 0, from (0.0.0) to (2.8.0) followed by the line segment from (2,8,0) to (1,1,2) 22 marks)
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3),...
→ (1 point) Let Vf-6xe-r sin(5y) +1 5e* cos(Sy) j. Find the change inf between (0,0) and (1, n/2) in two ways. (a) First, find the change by computing the line integral c Vf di, where C is a curve connecting (0,0) and (1, π/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 t 1, K) = dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily...
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1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
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Let C be the curve consisting of line segments from (0, 0) to (3, 3) to (0, 3) and back to (0,0). Use Green's theorem to find the value of [ xy dx + xy dx + y2 + 3 dy. Use Green's theorem to evaluate line integral fc2x e2x sin(2y) dx + 2x cos(2) dy, where is ellipse 16(x - 3)2 + 9(y – 5)2 = 144 oriented counterclockwise. Use Green's...