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 November 30th, 2012, 12:37 PM #1 Newbie   Joined: Nov 2012 Posts: 1 Thanks: 0 changing order of integration Hi! I'm solving this problem and I'm not sure how to solve it I have definite triple integral of function f(x,y,z). It's domain is set $M = \{0 I would like to get function g(z) = \int\int f(x,y,z) dxdy but I'm quite confused with borders of integration (and od course domain of the function g) -> Could you give me some help? Thanks in advance! --- -> and here goes my idea (but I'm not sure about it): - for each$z$and$y$I'm able to get an interval for$x$:$\max \left(0, \frac{z-2y^2+3ay}{y+a} \right) < x < \min \left( a , \frac{a^2 - 2y^2+2ay + z}{y} \right)$- therefore I can get function \int_max(...)^min(...) f(x,y,z)dxdydz = [h]_{\max(...)}^{\min(...)}$ - for each $z$ I'm able to say which values functions min/max takes - so the function g(z) could be sum of integrals of k(y,z) (the number of integrals and their domains depends on values of min/max function..) -> so, is it good idea or really wrong way of thinking about this problem? -> and what about domain of g(z)? (could it be [min_(x,y)f(x,y,z);max_(x,y)f(x,y,z)] ?) --- Once again thanks in advance! (and sorry for my English..  ). Have a nice day! Doxxik December 14th, 2012, 05:40 PM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: changing order of integration All you are told about x and y is that 0< x< a and 0< y< a so that the integrals, with respect to x and y, are from 0 to a. The result will be a function of z and its domain will be the possible values of z. What are the maximum and minimum values of the two functions bounding z on the square 0< x< a and 0< y< a? Tags changing, integration, order 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 OriaG Computer Science 1 March 1st, 2013 03:54 AM triplekite Calculus 1 December 3rd, 2012 12:30 PM FreaKariDunk Calculus 1 April 10th, 2012 06:41 PM Yooklid Real Analysis 3 June 17th, 2010 10:21 PM Gotovina7 Calculus 1 February 29th, 2008 09:30 AM

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