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 .
Evaluate the line integral ∫C.F·dr, where C is given by the vector function r(t).
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 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.
(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 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), ?) ,
(2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along the helical path r-costi + sintj+tk, 0St (3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2 (2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along...
(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,...
c. Let F : R³ → R³ be a vector field on R, given by the following function F(x, y, 2) = (x2)i + (y2)J + (xy)k. Calculate the flux of the field across the surface of the hemisphere, : [0, 1] × [0, 2x] → R³, where parametrized by the following function Þ(r, 0) = (r cos 0)i + (r sin 0) + (1 – 1²)!/2 k.
9. Evaluate the “vector valued” line integral 1.Podr Fodr where F(x, y, z) = (x, y, zy) TT and C is given by r(t) = (sint, cost, t), with N » 4. u sta