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Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (5x,5y); R = {(x,y): x² + y² ≤4}

Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (5x,5y); R = {(x,y): x² + y² ≤4}

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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a. The two-dimensional curl is. (Type an exact answer.) b. Set up the integral over the region R. Write the integral using polar coordinates, with r as the radius and as the angle. r dr de (Type exact answers.) Set up the line integral. Use the standard parameterization for a circle with t as the independent variable. ļ )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.) ⒸA. The integrals are not consistent. The double integral evaluates to results yields. OB. The integrals are consistent because they both evaluate to but evaluating the line integrals and adding the
Transcribed Image Text:a. The two-dimensional curl is. (Type an exact answer.) b. Set up the integral over the region R. Write the integral using polar coordinates, with r as the radius and as the angle. r dr de (Type exact answers.) Set up the line integral. Use the standard parameterization for a circle with t as the independent variable. ļ )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.) ⒸA. The integrals are not consistent. The double integral evaluates to results yields. OB. The integrals are consistent because they both evaluate to but evaluating the line integrals and adding the
Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (5x,5y); R = {(x,y): x² + y² ≤4}
Transcribed Image Text:Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (5x,5y); R = {(x,y): x² + y² ≤4}
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