Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y² - 5x²)i + (5x² + y²) j and curve C: the triangle bounded by y=0, x= 3, and y = x. The flux is

Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. = (5xy + 2y?) i+ (5x- 2y)j (1,1) F = x=y? C ? y =x (0,0)

Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 3₁ F = 2yi +5xj + z³k; C: the counterclockwise path around the perimeter of the triangle in the x-y plane formed from the x-axis, y- axis, and the line y = 5 - 6x

a) Draw 4 pictures showing all possible combinations of a vector field and a curve b) Compute the circulation and the flux

a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the flux of F = (x³, y³, z³) through any closed surface positive, negative, or zero?