Evaluate the line integral «+xy+y)ds where C is the path of the arc along the circle...
Problem 1 Evaluate the line integral / x2 ds, where C is the line segment from (3,0) to (0,4) in the xy-plane.
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
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)
Evaluate the line integral Sc(xy? + siny)dx, where C is the arc of the parabola x=y2 from (0,0) to (12,n).
(10) (8 points) Evaluate the line integral Scry ds, where C is the upper half of the circle r2 + y2 = 4.
The path integral of a function f(x, y) along a path e in the xy-plane with respect to a parameter r is given by 2. fex,y)ds= f(x),ye) /x(mF +y(t" dr , where a sr sb. (a) Show that the path integral of f(x, y) along a path c(0) in polar coordinates where r=r(0), α<θ<β, is Sf(r cos 0,rsin e) oN+( de. (b) Use this formula to compute the arc length of the path r 1+cos0, 0<0 27 The path integral...
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
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.
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation. 9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation.