Convert the given iterated integral from Cartesian coordinates to spherical coordinates. -1 4-x2-y2 zdzdydx 3x24 +3y2

Calculus 3 Module: Line Integral

Q\ Evaluate the iterated integral by converting to polar coordinates V2x-x2 Vx2 + y2 dy dx

Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 – cos (v)) sin (u), z = sin (v) at the image of a point (u, v) for –x < v < a and -a < u < a. (Write your solution using the form (*,*,*). Use symbolic notation and fractions where needed.) no = Identify this surface. ellipsoid hyperboloid torus cylinder

Verify if div(curl F) = 0 for = (x- y)i+ (x +y)j+zk. %3D

convert the integral from rectangular coordinates to spherical coordinates. DO NOT EVALUATE

calculate div(F) and curl(F). F = (xy, yz, y² – x³)

PLz don't take the answer of any other expert if u take i will give u thumb down so do by yourself

Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle with vertices (0,0), (11,0), and (10, 9) (in the positive direction).