Multivariable calculus

J. The general method for nding the area element dA = d1: dy in a different coordinate system age: where 3: = He, 1;) and y = 9(n, e) is given by the determinant of the Jacobian matrix, J(:e, y). (9:1: 8:1: m )=a(x,y)= a 3\" 1y 3(u,v) 6y 8y 6e at; In the case of polar coordinates, u = r and 'u = 9. Use the Jacobian to conrm that the area element in polar/ cylindrical coordinates is given by do: dy -+ 1' (11' d9. 1. Find the change of variables formula for triple integrals in cylindrical coordinates. You can either expand the ideas from the notes or extend your results from above