• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Iterated Integral Question

  • Thread starter s10dude04
  • Start date
1. Homework Statement

(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. Homework 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?
 
Last edited:
32,571
4,301
1. Homework Statement

(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. Homework 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?
Not at all, as far as I can see from your work. The first part asks you to sketch the region over which integration takes place. Have you done that? This region can be described pretty simply.
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)?
 

Related Threads for: Iterated Integral Question

  • Posted
Replies
4
Views
1K
Replies
1
Views
725
  • Posted
Replies
2
Views
4K
  • Posted
Replies
3
Views
2K
  • Posted
Replies
12
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top