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 = (-2y, -3x); R is the region bounded by y = sin x and y = 0, for 0≤x≤a. The two-dimensional curl is - 1(Type an exact answer.)b. Set up the integral over the region R.SSO dy dx00(Type exact answers.)Write the line integral for the y = 0 boundary.dt0(Type an exact answer.)Write the line integral for the y sin x boundary.dt...0(Type an exact answer.)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 toOB. The integrals are not consistent. The double integral evaluates to but evaluating the line integrals and adding the results yields

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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 = (-2y. -3x); R is the region bounded by y sin x and y=0, for 0≤x≤

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 = (-2y. -3x); R is the region bounded by y sin x and y=0, for 0≤x≤

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question

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 = (-2y, -3x); R is the region bounded by y = sin x and y = 0, for 0≤x≤
a. The two-dimensional curl is - 1
(Type an exact answer.)
b. Set up the integral over the region R.
SSO dy dx
00
(Type exact answers.)
Write the line integral for the y = 0 boundary.
dt
0
(Type an exact answer.)
Write the line integral for the y sin x boundary.
dt
...
0
(Type an exact answer.)
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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