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Evaluating Double Integrals: Switching the Order of Integration 
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#1
Oct2707, 03:23 PM

P: 8

1. The problem statement, all variables and given/known data
Evaluate the double integral by changing the order of integration in the iterated integral and evalutating the resulting iterated integral. 2. Relevant equations [tex]\int[/tex][tex]^{1}_{0}[/tex] [tex]\int[/tex][tex]^{1}_{x}[/tex] cos(x/y)dydx 3. The attempt at a solution I know how to solve a double integral after i've switched the order of integration, i'm having trouble with the acutal switching part The book we are using has one example in it regarding this, and it isn't very clear. If anyone would mind walking me through how to switch the order of integration, that'd be great Thanks in advance, Andy edit: The text for the integrals didnt come out well, to make it more clear, its the integral from 0  to  1 and the integral from x  to  1 


#2
Oct2807, 12:58 AM

HW Helper
P: 3,348

Why must you change the order? The integral is easily solvable as it is.



#3
Oct2807, 02:21 AM

HW Helper
PF Gold
P: 1,197

So, the area over which you're integrating is bounded in the x direction by the lines x=0 and x=1. Also, since the limits in y are from x to 1, the boundaries in the y direction are the lines y=x and y=1. Can you sketch the area now? From this, can you figure out how to switch the order of integration? 


#4
Oct2807, 02:27 AM

HW Helper
P: 3,348

Evaluating Double Integrals: Switching the Order of Integration



#5
Oct2807, 10:12 AM

P: 8

Ok, thanks! so if i'm not mistaken then, the new equation is:
[tex]\int[/tex][tex]^{1}_{0}[/tex] [tex]\int[/tex] [tex]^{y}_{0}[/tex] cos(x/y)dxdy ? 


#6
Oct2807, 12:16 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,533

Yes. In your original integral x ranged from 0 to 1 and, for each x, y ranged from x to 1. That is the triangle with vertices (0,0), (1,1) and (0, 1). In the opposite order, to cover that triangle, y must range from 0 to 1 and, for each y, x must rage from 0 to y.



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