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= (-4y, - 2x):...

Extracted 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= (-4y, - 2x): Ris the region bounded by y = sin x and y = 0, for 0sxSx. a. The two-dimensional curl is (Type an exact answer.) b. Set up the integral over the region R. dy dx (Type exact answers.) Write the line integral for the y =0 boundary. dt (Type an exact answer.) Write the line integral for the y ▪ sin x boundary. dt (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.