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: Use the given transformation to evaluate the integral

  1. Jul 17, 2012 #1
    ∫∫10xy(dA), where R is the region in the first quadrant bounded by the lines y=x/2 and y=2x/3 and by the hyperbolas xy=1/2 and xy=3/2

    The transformations given in the problem (these cannot be altered): x=u/v and y=v

    Relevant equations:

    The Jacobian - ∂(x,y)/∂(u,v)

    The attempt at a solution:

    y=(3/2)x: 2v^2=3u
    y=x/2: 2v^2=u
    xy=1/2: u=1/2
    xy=3/2: u=3/2

    After making the transformations, I get the following double integral:

    10∫(u from 1/2 to 3/2)∫(v from √(u/2) to √(3u/2)) (u/v)dvdu

    I feel like my transformations are suppose to result in basic bounds without variables, so I think I am doing this problem incorrectly and can't figure out any other way to go about it.
  2. jcsd
  3. Jul 17, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    That looks good to me.

    The transformation does simplify the region, even if it's not rectangular.

    Try the integration.
  4. Jul 17, 2012 #3
    Wonderful! I performed the integration and got 10ln(√3) and this was correct.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook