Q1: 4pnts Evaluate the following integrals along the given curve C. (a) (32) ds. C : The section of the parabola y = x2...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t (1)...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
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
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,...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
. 0 -15.55 points ZiICAnalysis3 5.1.011 Evaluate the line integrals G(x, y) dx, G(x, y) dy, and G(x, y) ds on the indicated curve C. G(x, y)-2xy; x-3 cos(t), y-3 sin(t), o s t s G(x, y) dx G(x, y) dy G(x, y) ds Practice Another Version We were unable to transcribe this image
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), ?) ,
I do NOT need part a. I really need help on b,c,d,and e though! Thank you 2. Evaluate the line integral where C is the given curve: BE SURE THAT YOU PARAMETERIZE EACH CURVE! (a) ez dr where C is the arc of the curve z = y3 from (-1,-1) to (1,1); (b) 2,2 d_T + y2 dy where C consists of the arc of the circle x2 + y2-4 from (2,0) to (0,2) followed by the line segment from...
No 3 putin uhd e integral lound a r the val- 0 VIIl, 81. EXERCISES Compute the curve integrals of the vector field over the indicated curves. (x,y)=(x2-2xy,y2-2xy) along the, parabola y=x2 from (-2,4) to 2. 0x, y, xz - y) over the line segment from (0,0, 0) to (1, 2, 4), 3, Let r (x2 y2)1/2 Let F(X)-X. Find the integral of F over the circle of radius 2, taken in counterclock wise direction. 4. Let C be a...
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....