52:36 I think that x=r*sin(theta) and y=r*cos(theta) are vice versa when the determinant of the Jacobian matrix is computed. dx/dr will compute to d(r*sin(theta))/dr=sin(theta), not cos(theta). When taking the partial derivative with respect to r, sin() in x=r*sin(theta) will be unchanged.
52:36 I think that x=r*sin(theta) and y=r*cos(theta) are vice versa when the determinant of the Jacobian matrix is computed. dx/dr will compute to d(r*sin(theta))/dr=sin(theta), not cos(theta). When taking the partial derivative with respect to r, sin() in x=r*sin(theta) will be unchanged.
Yeah I agree, you can see on timestamp 42:12 You can see that X = r*cos(theta) and Y = r*sin(theta). That solves the confusion.
Fantastic!
Very confusing to use f(x) as a PDF name, since we are integrating the f(x)...