I need help with these:
Which (if any) of the following vector fields are conservative: Frightarrow (x, y) = exyirightarrow + ex+yjrightarrow Frightarrow (x, y) = 2x cos y irightarrow - x2 sin yjrightarrow Determine if the field Frightarrow (x, y, z) = cos xz, sin yz, xy sin z) is conservative. Let Frightarrow (x, y) = xy2irightarrow + x2yjrightarrow. Evaluate intC Frightarrow·dsrightarrow where C is the upper half of the circle of radius 1 centered at the origin orientated counterclockwise. Find a potential function for Frightarrow (x, y, z) = yz2, xz2 - z, 2xyz - y . Use part (a) to evaluate intC Frightarrow·dsrightarrow where C is any path in space from P= (1, 2, 3) to Q = (3, 2, 1). Let Frightarrow (x, y, z) = z2/xirightarrow + z2/yjrightarrow + 2z ln xy krightarrow. Evaluate intC Frightarrow ·dsrightarrow Where C is the path of straight line segments from P = (1, 2, 1) to Q = (4, 1, 7) to R = (5, 11, 7), and then back to P. (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Suppose intT nablaphi · dsrightarrow = 1 where T is the path from P = (-2, 1) to Q = (2, 1) along the top half of the ellipse 3x2 +11y2 = 23. Determine the value of intB nablaphi · dsrightarrow where B is the path from P to Q along the bottom half of that ellipse.