Evaluate the line integral ∫ F *dr
where C is given by the vector function r(t).
F(x, y, z) = (x + y2) i + xz j + (y + z) k,
r(t) = t2i + t3j − 2t k, 0 ≤ t ≤ 2
Evaluate the line integral ∫ F *dr where C is given by the vector function r(t)....
Evaluate the line integral ∫C.F·dr, where C is given by the vector function r(t).F(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t3 i- t3j + tk, 0 ≤ t ≤ 1 .
(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 -...
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....
Evaluate the line integral Sc Fodr where C is given by the vector function (EJ=<t2, to, z> for ost 43 and (x, y, z)=(x+ya, xz, y+ z7.
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), ?) ,
(1 point) Evaluate the line integral ScF. dr, where F(x, y, z) = -4xi – 4yj + 5zk and C is given by the vector function r(t) = (sin t, cost, t), osts 31/2. 4
please be clear as possible. thanks 2. Evaluate the line integral where C is the given curve: BE SURE THAT YOU PARAMETERIZE EACH CURVE! (a) e dr where C is the are of the curve r y' from (-1,-1) to (1, 1): (b) dr dy where C conusists of the arc of the circle 2+ 4 from (2.0) to (0.2) followed by the line segment from (0.2) to (4,3) (c) y': ds where C is the line segment from (3,...
Please help! Question 5 25 (5.1) Sketch some vectors in the vector field given by F(r, y) 2ri + yj. (3) (5.2) Evaluate the line integral fe F dr, where F(r, y, 2) = (x + y)i + (y- 2)j+22k and C is given by the vector function r(t) = ti + #j+Pk, 0 <t<1 (4) costrt>, 0St<1 (5.3) Given F(r, y) = ryi + yj and C: r(t)=< t + singat, t (3) (a) Find a function f such...
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = (-y+z)i + (x – z)j + (x – y)k. S is the surface z = V1 – 22 – y2, and C is the boundary of S with counterclockwise orientation (from above).
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)