1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Evaluating a double integral

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following double integral:
    ∫ ∫ R sin (x/y) dA

    where R is the region bounded by the y axis, y=pi and x=y^2

    2. Relevant equations

    as in problem statement

    3. The attempt at a solution

    Well I started this question by drawing the area to be evaluated. From this I chose my limits of integration, however I feel this may be where I am going wrong. I used ∫ (upper y=pi lower y=0) dy and ∫ (upper x=y^2 lower x=0) dx.
    Im not sure if this is right first of all, and secondly, sin (x/y) is really tripping me up. This is because when I treat a variable as constant, where is it going. For example if I firstly evaluate sin (x/y) dy, i'm not sure of the result.
  2. jcsd
  3. Apr 26, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi ilovemath88! Welcome to PF :smile:

    (have an integral: ∫ and a pi: π and try using the X2 and X2 tags just above the Reply box :wink:)

    Yes, your limits, ∫0π0y2 are correct.

    As you say, you have to treat one variable as a constant when you integrate wrt the other …

    so which is easier to integrate first, sin(x/y)dx or sin(x/y)dy ? :wink:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook