Calculus 16.4 Green's Theorem

[@juniorcyans2988]

25:15 How did you get (y^2-x^2)/(x^2+y^2)^2 from F(x,y) ? I don’t understand the way how you found dP and dQ. Thanks a lot!

[@asherroberts]

F=Pi+Qj, so P=-y/(x^2+y^2) and Q=x/(x^2+y^2). The partial derivative of Q with respect to x is then (y^2-x^2)/(x^2+y^2)^2 by the quotient rule, which is the same as the partial derivative of P with respect to y.

[@juniorcyans2988]

@@asherroberts Oh I forgot the quotient rule! Thanks a lot!

[@sufitech4643]

very helpful Can you PROOF OF GREEN’S THEOREM FOR THE CASE IN WHICH D IS A SIMPLE REGION this give in the same book above example 1