Calculus Calculus Math Forum

 October 31st, 2017, 03:21 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 double integral problem Find the area of z = x^2 - y^2 that lies inside x^2 + y^2 = a^2. Here is my solution. But I am stuck here because I don't know how to calculate this mess... $\displaystyle x = u, y = v, z = u^2-v^2$ $\displaystyle \int_{-a}^{a} \int_{- \sqrt{a^2-u^2}}^{ \sqrt{a^2-u^2}} \sqrt{4u^2+4v^2+1} ~dv ~du$ October 31st, 2017, 05:40 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,468 Thanks: 1342 you've confused yourself using u's and v's but otherwise what you've done is correct. however.... when you see $x^2 + y^2 = a^2$ you should immediately be thinking cylindrical coordinates. here we have $\displaystyle \int_0^{2\pi}\int_0^a~\sqrt{4r^2 + 1}~r~dr~d\theta$ and this is trivial to integrate. Thanks from topsquark and zollen Tags double, integral, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post harley05 Calculus 5 May 18th, 2014 07:51 PM unwisetome3 Calculus 0 May 13th, 2014 05:49 AM krampon Calculus 1 July 1st, 2013 07:21 AM Beevo Calculus 2 November 26th, 2012 02:44 PM j_bloggs Calculus 2 March 16th, 2010 01:34 AM

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