Find the circulation and flux for the field F(x, y) = (y – 6x² , x+y²) around and across the triangle given by y = 0, y = x, and x = 1.

Let I be the flux of G = (4e³,9x³ex⁹, 0) through the upper hemisphere S of the unit sphere. (a) Find a vector field A such that curl(A) = G. (b) Calculate the circulation of A around as. (c) Compute I, the flux of G through S. (a) A = (b) √ A · ds = (c) I =

+25y²,0, 10- through the surface 3 Find the outward flux of F = =1.

Let f(x, y) = 7x cos (y). Find the conservative vector field F, which is the gradient of f. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) F = (7 cos (y).-7x sin(y) Evaluate the line integral of F over the upper half of the unit circle centered at the origin, oriented clockwise. (Give an exact answer. Use symbolic notation and fractions where needed.) C F. dr = Incorrect 12 Question Source: Rogawski 4e Calculus Early Transcendentals Publisher: W.H. Freema 5.02. D