This Test: 18 pts possible 5 of 18 (1 comnplete) the foillowing vector field and region. Check for agreement Evaluat...
Consider the following region 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= (2x-2y); R=(x,y): x2 + y²59 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 O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
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 the flux form of Green's Theorem and check for consistency. c. State whether the vector field is source free. F = (8xy,9x2 - 4y?); R is the region bounded by y = x(6 - x) and y=0. .- a. The two-dimensional divergence is 0 b. Set up the integral over the region. dy dx 0 Set...
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 = (3y, - 3x); R is the triangle with vertices (0,0), (1,0), and (0,2). . a. The two-dimensional curl is (Type an exact answer.) b. Set up the integral over the region R. JO dy dx 0 0 (Type exact answers.) Set up the line integral for the line...
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 the circulation form of Green's Theorem and check for consistency. c. State whether the vector field is conservative. F-3y,3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 1) a. The two-dimensional curl is D (Type an exact answer, using π as needed.) b. Set up the integral over the region R. dy...
13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II curve ll surface is: and: Divergence Theorem The vector field |l curve l surface is: (b) For each of the following, choose all correct answers from the list below that can be used to evaluate the given integral. List items may be used more than once. i....
Show that the differential form in the integral is exact. Then evaluate the integral. (3,0.1) sin y cos x dx + cos y sin x dy + 8 dz (1,0,0) Compute the partial derivatives. OP ON dy dz Compute the partial derivatives. дМ OP 0 dx Compute the partial derivatives. ON OM Select the correct choice below and fill in any answer boxes within your choice. 13.0.1 sin y cos x dx + cos y sin x dy + 8...
Show that the differential form in the integral is exact. Then evaluate the integral. (0.4.4) sin y cosx dx + cos y sin x dy + 4 dz (1,0,0) s Compute the partial derivatives. ӘР ON ay dz Compute the partial derivatives. OM ap dz Compute the partial derivatives. ON OM ду Select the correct choice below and fill in any answer boxes within your choice. O A sin y cos x dx + cos y sin x dy +...
Show that the differential form in the integral is exact. Then evaluate the integral. (2.0.2) | sin y cosx dx + cos y sin x dy +7 dz (1,0,0) Compute the partial derivatives. OP ON ду az Compute the partial derivatives OM OP dz Compute the partial derivatives. ON dy Show that the differential form in the integral is exact. Then evaluate the integral. (2.0,2) S siny cosx dx + cos y sin x dy +7 dz (1.0,0) Compute the...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...