integrals below are equivalent. According to Green's theorem, the two x4 dx+xy dy= y-0 dA Question 9: Calculate bot...
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where C is the triangle with vertices (0,0), (1,0) y (1,2)
Compute the Curl V x F = Qx-P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) fcx* dx + xy dy cow around the triangle with vertices (0,0), (1,0) and (0,1).
Green's Theorem )dy - (4y2 ex)dx Evaluate Y Here, y is the path along the boundary of the square from (0,0) to (0,1) to (1,1) to (1,0) to (0,0) State Green's Theorem in its entirety. Sketch the curve, y. Indicate the given orientation on the curve. Explain in detail how all the conditions of the hypothesis of the theorem are satisfied. Use Green's Theorem to evaluate the given integral. Simplify your answer completely. Green's Theorem )dy - (4y2 ex)dx Evaluate...
Consider the following region R and vector field a. Evaluate both integrals in Green's Theorem - Circulation Form and check for consistency. b. Is the vector field conservative? 7) (16 points) F = 〈x4, xy〉, R is the triangular region with vertices (0,0), (1,0) and (0,1). Consider the following region R and vector field a. Evaluate both integrals in Green's Theorem - Circulation Form and check for consistency. b. Is the vector field conservative? 7) (16 points) F = 〈x4,...
-/1.42 POINTS LARCALC10 15.4.003. Verify Green's Theorem by evaluating both integrals [x?dx + x? dy = f S (x om) da for the given path. C: square with vertices (0,0), (3, 0), (3, 3), (0, 3) { y dx + x² dy =
se Green's theorem in order to compute the line integral ∮C(ex2−y3)dx+(sin(y3)+x4)dy∮C(ex2−y3)dx+(sin(y3)+x4)dy where CC is the boundary of the square [0,1]×[0,1][0,1]×[0,1] traversed in the counterclockwise way.
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
5. (4 points) Calculate integral $.264 + z sin y)dx + (x? cos y − 3yjº)dy along triangle with vertices (0,0), (1,0) and (1,1), oriented counterclockwise, using Green's theorem.
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise. 12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
2. [-/10 Points] DETAILS LARCALC11 15.4.007. 0/6 Submission Verify Green's Theorem by evaluating both integrals |_ ? dx + x? dy = f S (mmen med dA for the given path. C: square with vertices (0,0), (2, 0), (2, 2), (0, 2) Je v2 dx + x² ay = an ax дм ay dA Need Help? Read It Talk to a Tutor