How do you solve the double integral

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Homework Help Overview

The discussion revolves around solving a double integral of the function cos(u/v) with specified limits for u and v. The limits for u are from -v to v, and for v, they are from 1 to 2. The subject area involves calculus, specifically double integrals and trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods for integrating the function, including integration by parts and treating v as a constant during integration. There are questions about the complexity of the resulting expressions and requests for clarification on specific steps taken in the integration process.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and seeking further explanations. Some guidance has been offered regarding the integration process, but no consensus has been reached on the best approach or the correctness of the results obtained.

Contextual Notes

Participants mention different calculus resources, indicating varying levels of familiarity with the material. There is also a sense of confusion regarding the integration process and the resulting expressions, which may affect their understanding of the problem.

fk378
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Homework Statement


How do you solve the double integral of cos(u/v) dudv, if the limits of u are v and -v, and the limits of v are 1 and 2?

I tried doing it by parts but I didn't get it...
 
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fk378 said:

Homework Statement


How do you solve the double integral of cos(u/v) dudv, if the limits of u are v and -v, and the limits of v are 1 and 2?

I tried doing it by parts but I didn't get it...

what so tough about it?

int {v = 1 to 2}{u=-v to v} cos(u/v) du.dv

treat v as constant and integrate cos, put the limits in (get something like sin(1) ) ..

I did really quickly and had something like 3 sin(1)

P.S. are you using glyn james .. ?
 


If I integrate cos first and treat v as a constant, then I get v(sin(u/v))...isn't that messy? Can you show me what you did or explain it further please?

And I am using Stewart's calc, not glyn
 


fk378 said:
If I integrate cos first and treat v as a constant, then I get v(sin(u/v))...isn't that messy? Can you show me what you did or explain it further please?

And I am using Stewart's calc, not glyn

it goes from -v to v

so

v (sin(v/v)-sin(-v/v))
 

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