WITH ALL STEPS SHOWN ay+y?)dx- xdywhere C is the closed curve 3. Verify Green's Theorem in the plane for of the reg...
PLEASE USE GREEN'S THEOREM
8. Verify Green's Theorem for f (64 – 3y2 + x) dx + yzºdy where C is shown below by (a) computing the line integral directly and (b) using Green's Theorem to compute the line integral . 5 (1,5) 3 (1,3) 2.
10. [8 points] Use Green's Theorem to evaluate the line integral Sexy dx + (x2 + y) dy, where the closed curve C determined by y=x2 and y - =2 between (-1,1) and (2, 4). Sketch the curve and the region enclosed by the curve.
I Verify Green, Theorem for the field F(x, y) = (x - y) + + x 7 and the region R bounded by the unit circle x² + y² = 1. b) Use the Green's theorem to evoluate the line integral 3 y dx + 2xdy where C is the boundary of the region Os x a , Os y < siax orciented counter clockwise. (Answer : -2)
Use Green's Theorem to evaluate the line integral. (x - 97) dx + (x + y) dy C: boundary of the region lying between the graphs of x2 + y2 = 1 and x2 + y2 = 81 x-9
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer
4. -15 points Use Green's theorem for flux to evaluate the line integra ds . (6ху, y2-x2) and C is the positively oriented boundary curve of the region bounded by y F 0 and y x(4-x). Submit Answer
(7) Green's Theorem for Work in the Plane F(x, y) =< M, N >=< x, y2 > C: CCW once about y = vw and y = x W = | <M,N><dx,dy>= | Mdx + Ndy CZ CZ (70) Parametrize the path Cy: along the curve y = vw from (1,1) to (0,0) in terms of t. (70) Use this parametrization to find the work done. (7e) Confirm Green's Theorem for Work. (7) Green's Theorem for Work in the Plane...
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3. Use Green's Theorem to calculate Je y tan’t dx + tan x dy, where C is the circle x2 + (y + 1)2 = 1. 4. Evaluate the surface integral SS. (x + y)dS where o is the portion of the plane z = 6 - 2x – 3y in the first octant.
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
Evaluating using Green's theorem
(4x^3+sin(y^2))dy-(4y^3+cos(x^2))dx where C is the boundary of the
region x^2+y^24
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We were unable to transcribe this image3. EVALUATE USING GREEN'S THEOREM (4x++sinyydy –(4y+cosx2) dx, WHERE C IS THE BOUNDARY OF THE REGION X+Y24.
1. [-/10 Points] DETAILS LARCALC11 15.4.005. 0/6 Submissions Used Verify Green's Theorem by evaluating both integrals Ja yax+ y2 dx + x2 dy дм ду for the given path. C: boundary of the region lying between the graphs of y = x and y = x2 + x2 dy AS COMO an дх aM ду dA =