Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (-4x, -4y); R=(x,y): x² + y² ≤ 16 a. The two-dimensional divergence is -8. (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates, with r as the radius and 0 as the angle. 24 0 Set up the line integral. Let the parameter be t=0, where is the angle measured counterclockwise from the positive x-axis. 0 2π S 0 (-8) r dr de (Type exact answers.) dt ((Type exact answers.)
Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (-4x, -4y); R=(x,y): x² + y² ≤ 16 a. The two-dimensional divergence is -8. (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates, with r as the radius and 0 as the angle. 24 0 Set up the line integral. Let the parameter be t=0, where is the angle measured counterclockwise from the positive x-axis. 0 2π S 0 (-8) r dr de (Type exact answers.) dt ((Type exact answers.)
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:Consider the following region R and the vector field F.
a. Compute the two-dimensional divergence of the vector field.
b. Evaluate both integrals in Green's Theorem and check for consistency.
F = (-4x, -4y); R=(x,y): x² + y² ≤ 16
a. The two-dimensional divergence is -8. (Type an exact answer.)
b. Set up the integral over the region. Write the integral using polar coordinates, with r as the radius and 0 as the angle.
24
0
Set up the line integral. Let the parameter be t=0, where is the angle measured counterclockwise from the positive x-axis.
2x
0
S
0
(-8) r dr de (Type exact answers.)
dt ((Type exact answers.)
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