For the vector field \((x^3 z^2, 0, -x^2 z)\), evaluate the line integral on the closed curve made by a square in the \((x, z)\) plane with corners at \((1, 0, 1)\), \((-1, 0, 1)\), \((-1, 0, -1)\), \((1, 0, -1)\) in the counterclockwise direction.

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Answered: For the vector field (x³z², o, -x²z),…

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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5) Find the flux of F = (-2y, -x) on the circle of radius 2 centered at the origin. Use the vector field grapher shown in class and cut and paste the vector field here. Before you calculate the flux do you expect your answer to be positive, negative, or zero?
Sketch the vector field of F (-y, 0) in the xy-plane. Be sure to draw enough vectors so that the pattern of the magnitude of the vectors and the direction of the vectors is clear. It is not required to label any points or vectors.
A child living in the ry-plane climbs a ladder from (0, 0) to (1, 1), slides down to (2,0) along the parabolic path y = (x – 2)?, and then walks back to (0, 0) along the r-axis. Find the work done by the vector field F(x, y) = (2x – y², y³) in moving the child along her path. Select one: a. 4 21 b. 8 15 C. 4 d. 7 е. -1
For the vector field (x, y, 2) evaluate the line integral along the curve made of three adjacent segments. from (1,2,8) to (3,0,3) from (3, 0,3) to (-1,0, 2) from (-1, 0, 2) to (0,0,7)
Consider the vector field v(x) j+6k. a) Calculate fv• dr, where I is the straight line from (4,0,4) to (0,4,8). b) Calculate fu• dr where C'is the curve from (4,0,4) to (0,4, 8) in the first quadrant given by x? + 4y? = 22 ,x + z = 8.
Show that Green's Theorem holds for the vector fieldF(x, y)=(x +y, 3x) at a square of side 2.

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For the vector field (x³z², o, -x²z), evaluate the line integral on the clase curve made by a square in the (x, 2) plane with corners at (1,0,1), (-1,01), (-1,0, -1), (1, 0,-1) in the counterclockwise direction.