Let C be the helix that winds around the cylinder x2+y? = 1 (counterclockwise viewed from the positive z-axis looking down on the xy-plane), starting at (1,0,0), winding around the cylinder once, and ending at the point (1,0, 1). Compute the line integral of the vector field F(x, y, z) = (-y, x, z²). (Hint: this vector field is not conservative.)

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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Needed to be solved part b completely
(a) Compute the arc length of the curve r(t) = (t2, 3, t) between the points (0, 3,0) and
(1, 3, 1/3).
(b) Let C be the helix that winds around the cylinder x?+y?
from the positive z-axis looking down on the ry-plane), starting at (1,0,0), winding
around the cylinder once, and ending at the point (1,0, 1).
= 1 (counterclockwise viewed
Compute the line integral of the vector field F(x, y, z) = (-y, x, z²). (Hint: this vector
field is not conservative.)
Transcribed Image Text:(a) Compute the arc length of the curve r(t) = (t2, 3, t) between the points (0, 3,0) and (1, 3, 1/3). (b) Let C be the helix that winds around the cylinder x?+y? from the positive z-axis looking down on the ry-plane), starting at (1,0,0), winding around the cylinder once, and ending at the point (1,0, 1). = 1 (counterclockwise viewed Compute the line integral of the vector field F(x, y, z) = (-y, x, z²). (Hint: this vector field is not conservative.)
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