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5. Evaluate the integral of f along a contour y where f and y are given...
Complex Analysis I need it asap Evaluate the integral of f along a contour y where f and 7 are given as follows. (a) f(x+iy) = eyel-ix along , a positively oriented ellipse determined by the equation r = cos(20) +2. [6] (b) f(z) = 223(24 – 1)-2 along y(t) =t+iVt where 0 <t<l. [10]
Yes find Integral in Complex analysis Or Complex Contour Integration 5. Evaluate the integral of f along a contour y where f and y are given as follows. (a) f(x+iy) = eyel-ix along y, a positively oriented ellipse determined by the equation r = cos(20) +2. (b) f(z) = 223 (24 – 1)-2 along y(t) =t+iVt where 0 <t<1. [10] [6]
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 4 sin(y) dx + 4x cos(y) dy C is the ellipse x2 + xy + y2 = 49 Ic
Use Green's Theorem to evaluate the line integral along the given positively oriented curve I = Sc (2y + 7eV*)dx + (3x + cos(y2))dy, where the curve C is the boundary of the region enclosed by the parabolas y = 9x2 and x = y2
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
could u please solve them all Thanks :) (15 points) Evaluate the given integral along positively oriented curve 2 and y2 where C is the boundary of the region enclosed by the parabolas y # (Hint: Use Green Theorem). (15 points) Let F = (6fpi + (2x3jj + .k be given. (a) Evaluate f F-dr along the plane curve y = 12 fronn (0.0.0) to (2,4,0). b) Evaluate, curl(F), div(F) and div(curl(F)) (15 points) Evaluate the given integral along positively...
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,...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Evaluate line integral ( F. dr where C is any positively oriented simple closed curve that encloses the origin by using a circle of radius r, and r is small enough so that the circle lies entirely inside C given F(x, y) = ? 1)_ 2xyi +(y2 – xº)j Ans (x² + y²)