SimReal: Mathematics - Vector Calculus - Green's Theorem - Example 001 [Main Menu] [Calculator] [Sim Normal] [Sim Tangential]
 We are going to find the solution of the following integral: ʃxydy-y2dx along the square with corners (0,0), (1,0), (1,1), (0,1). The normal form of Green's theorem: ʃF·nds = ʃF1dy-F2dx = ʃʃ∇·FdA We are using the normal form of the Green's theorem with the vector field: F = [F1,F2] = [xy,y2] Use the big scrollbar in the simulation window to compute the left side of Green's theorem and convince yourself that the answer is 3/2. Mark the checkbox 'CurlDiv' to visualize the computation of the right side of Green's theorem and convince yourself that this will give the same answer.

 We are going to find the solution of the following integral: ʃxydy-y2dx along the square with corners (0,0), (1,0), (1,1), (0,1). The tangential form of Green's theorem: ʃF·Tds = ʃF1dx+F2dy = ʃʃ(∇xF)·kdA We are using the tangential form of the Green's theorem with the vector field: F = [F1,F2] = [-y2,xy] Use the big scrollbar in the simulation window to compute the left side of Green's theorem and convince yourself that the answer is 3/2. Mark the checkbox 'CurlDiv' to visualize the computation of the right side of Green's theorem and convince yourself that this will give the same answer. 