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Iterated Integral Question 
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#1
Mar1909, 08:46 AM

P: 2

1. The problem statement, all variables and given/known data
(a) For the iterated integral \\cos(x/y)dydx (inner limits x to 1, outer limits 0 to 1) sketch the region in the plane corresponding to the double integral this interated integral evaluates. (b) Evaluate the double integral by changing the order of integration in the iterated integral and evaluating the resulting iterated integral. 2. Relevant equations 3. The attempt at a solution Taking the integral of cos(x/y) with respect to y gives you sin(2x/y^2) no? Then you evaluate from x to 1, which would be sin(2x)sin(2/x)? Then doing the integral of that gives ********? Am I heading in the right direction? 


#2
Mar1909, 09:17 AM

Mentor
P: 21,215

For the second part, how to you go from [itex]\int cos(x/y)dy[/itex] to sin(2x/y^2)? If you check this work by differentiating sin(2x/y^2) with respect to y, do you get cos(x/y)? 


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