THESE QUESTIONS ARE NOT TOPICS OF PHYSICS. THEY ARE TOPICS OF MATH ADVANCED.
. Evaluate the fulówing intógrals: tle ioibwai erdz c-boundary ofe square with sides; z ±2、y= ±2...
P1: Let the contour C denote the boundary of a square whose sides lie along the lines x = +- 2, y= +-2, running counter-clockwise. Evaluate each of these integral Let the contour C denote the boundary of a square whose sides lie along the lines x = ±2 and y 2, running counter-clockwise. Evaluate each of these integrals: cos(z) (2-%)2 cosh z Let the contour C denote the boundary of a square whose sides lie along the lines x...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b. Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward. C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
(10 pts) Evaluate where C is the boundary of the square with vertices (0,0), (1,0),(0,1) and (1, 1) oriented clockwise. (10 pts) Evaluate where C is the boundary of the square with vertices (0,0), (1,0),(0,1) and (1, 1) oriented clockwise.
2. (a) Sketch the region of integration and evaluate the double integral: T/4 pcos y rsin y dxdy Jo (b) Consider the line integral 1 = ((3y2 + 2mº cos x){ + (6xy – 31sin y)ī) · dr where C is the curve connecting the points (-1/2, 7) and (T1, 7/2) in the cy-plane. i. Show that this line integral is independent of the path. ii. Find the potential function (2, y) and use this to find the value of...
Evaluate the integral [c F.dr. F(x, y) = (x + y) i + (3x - cos y) j where is the boundary of the region that is inside the square with vertices (0,0), (4,0),(4,4), (0,4) but is outside the rectangle with vertices (1, 1), (3,1),(3,2), (1,2). Assume that C is oriented so that the region R is on the left when the boundary is traversed in the direction of its orientation.
1. Let F(x, y, z) = (-y + ,2-2,2-y), and let S be the surface of the paraboloid 2 = 9-32 - v2 for 2 > 0. oriented by an upward pointing normal vector. Note that the boundary of S is C, the circle of radius 3 in the xy-plane. Verify Stokes' Theorem by computing both sides of the equality: (a) (1 Credit) || (D x F). ds (b) (1 Credit) $F. dr
Thank you! xdy - ydx ф 30v2 where c is the boundary of the 3 Evaluate the line integral 1 segment formed by the arc of the circle x2 +y2-4 and the chord y-2-1 for x 2 0. xdy - ydx ф 30v2 where c is the boundary of the 3 Evaluate the line integral 1 segment formed by the arc of the circle x2 +y2-4 and the chord y-2-1 for x 2 0.