The path integral of a function f(x, y) along a path e in the xy-plane with...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
A force acting on a particle moving in the xy-plane is given by F = (2x3y4i+x2y3j), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x=5.00 m and y = 5.00 m as shown in the figure. Calculate the work W = F(r) dr done by F on the particle as it moves along a) The purple path b) The red path
Question 22 1 pts Compute the path integral of F = (y,x) along the line segment starting at (1,0) and ending at (3, 1). Question 23 1 pts Consider the vector field F= (1, y). Compute the path integral of this field along the path: start at (0,0) and go up 2 units, then go right 3 units, then go down 4 units and stop. Question 24 1 pts Compute Ss(-y+ye*y)dx + (x + xey)dy, where S is the path:...
Evaluate the line integral «+xy+y)ds where C is the path of the arc along the circle given by x2 + y2 = 9, starting at the point (3,0) going counterclockwise making an inscribed angle of a The line integral equals (45-72*sqrt(2))/8 Submit Answer Incorrect. Tries 1/8 Previous Tries
10 Given the double integral 4(x+ y)e dy dx, where R is the triangle in the xy-plane with vertices at (-1, 1), (1, 1) and (O,0). Transform this integral into J g(u.)dv du by the transformations given by 스叱制一想ル r}(u+v), y (u + v), y =-(u-v). Then, Evaluate the integral." (u-v). Then, Evaluate the integral. r
10 Given the double integral 4(x+ y)e dy dx, where R is the triangle in the xy-plane with vertices at (-1, 1), (1, 1)...
Evaluate the Surface Integral, double integral F*ds, where F = [(e^x)cos(yz), (x^2)y, (z^2)(e^2x)] and S is a part of the cylinder 4y^2 + z^2 =4 that lies above the xy plane and between x=0 and x=2 with upward orientation (oriented in the direction of the positive z-axis). ASAP PLEASE
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.
(a) The Cartesian coordinates of a point in the xy-plane are (x, y) = (-3.44, -2.64) m. Find the polar coordinates of this point. r = m θ = ° (b) Convert (r, θ) = (4.73 m, 36.1°) to rectangular coordinates. x = m y = m
2. Determine the work done by force F along the path C, that is, compute the line integral SF. dr from point A to point B. You need to find the parameterization of the curve C с and use it to find the line integral: Work = [F-di =[F(F(t).F"(t)dt Use F = (-yx) { +(x²) j in Newtons. and use a = 3 meters in the figure. Parameterization of a circle: Remember that for a circle: r(t) = [rcos(t) rsin(t)...
3. Calculate F. dr for F(x, y) =<x,y> using only one integral where is the path shown below. 4 -3 -2 -1 2 3