Use Stokes's theorem to evaluate OF.dr for the given F and C. (c) F(x, y, z) = xzi+ xyj– 3xz k, C : the line segment around the plane 2x + y + z = 2 that lies in the first octant with the orientation counterclockwise looking from above. (d) F(x, y,z) = 3y i– 2xj– 4x k, C : the ellipse obtained from the intersection between the cylinder x2 + y² = 4 and the plane z = x with the orientation counterclockwise looking from above.
Use Stokes's theorem to evaluate OF.dr for the given F and C. (c) F(x, y, z) = xzi+ xyj– 3xz k, C : the line segment around the plane 2x + y + z = 2 that lies in the first octant with the orientation counterclockwise looking from above. (d) F(x, y,z) = 3y i– 2xj– 4x k, C : the ellipse obtained from the intersection between the cylinder x2 + y² = 4 and the plane z = x with the orientation counterclockwise looking from above.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:F.dr for the given F and C.
Jc
Use Stokes's theorem to evaluate
(с) F(x, у, 2) — хzі+ хуј-3xz k,
C : the line segment around the plane 2x + y +z = 2 that lies in the first octant with
the orientation counterclockwise looking from above.
(d) F(x. у, 2) 3D Зуi — 2хј—4х k,
C : the ellipse obtained from the intersection between the cylinder x2 + y?
the plane z = x with the orientation counterclockwise looking from above.
4 and
||
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