Calculate the surface area of the part of the sphere x^2 + y^2 + z^2 = 1 that is contained in the lemniscata (x^2 + y^2)^2 = x^2 - y^2
I solved this quickly but i cant seem to get the same answer given in the book, And i would like to know which is the correct one. thanks in advance to anyone that helps.
the area element of a sphere given in x,y is
integrating it over the are of the lemniscata:
when i change to polar coordinates
i get
eventually solving and getting the wrong answer, what am i doing wrong?