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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 = (3x, 3y); R = (x,y): x² + y² ≤9 a. The two-dimensional divergence is. (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates, with r as the radius and 8 as the angle. Sr dr de (Type exact answers.) 0 0 Set up the line integral. Let the parameter be t=0, where 0 is the angle measured counterclockwise from the positive x-axis. Sdt ((Type exact answers.) 0 Evaluate these integrals and check for consistency. Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an exact answer.) O A. The integrals are consistent because they both evaluate to B. The integrals are not consistent. The double integral evaluates to but evaluating the line integrals and adding the results yields

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 = (3x, 3y); R = (x,y): x² + y² ≤9 a. The two-dimensional divergence is. (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates, with r as the radius and 8 as the angle. Sr dr de (Type exact answers.) 0 0 Set up the line integral. Let the parameter be t=0, where 0 is the angle measured counterclockwise from the positive x-axis. Sdt ((Type exact answers.) 0 Evaluate these integrals and check for consistency. Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an exact answer.) O A. The integrals are consistent because they both evaluate to B. The integrals are not consistent. The double integral evaluates to but evaluating the line integrals and adding the results yields

Advanced Engineering Mathematics
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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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 = (3x,3y); R = (x,y): x² + y² ≤9 C... a. The two-dimensional divergence is. (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates, with r as the radius and 8 as the angle. Sr dr de (Type exact answers.) 00 Set up the line integral. Let the parameter be t = 0, where 0 is the angle measured counterclockwise from the positive x-axis. dt ((Type exact answers.) Evaluate these integrals and check for consistency. Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an exact answer.) OA. The integrals are consistent because they both evaluate to OB. The integrals are not consistent. The double integral evaluates to , but evaluating the line integrals and adding the results yields
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 = (3x,3y); R = (x,y): x² + y² ≤9 C... a. The two-dimensional divergence is. (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates, with r as the radius and 8 as the angle. Sr dr de (Type exact answers.) 00 Set up the line integral. Let the parameter be t = 0, where 0 is the angle measured counterclockwise from the positive x-axis. dt ((Type exact answers.) Evaluate these integrals and check for consistency. Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an exact answer.) OA. The integrals are consistent because they both evaluate to OB. The integrals are not consistent. The double integral evaluates to , but evaluating the line integrals and adding the results yields
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