1. Not finding help here? Sign up for a free 30min 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!

Integration of multiple variables

  1. Mar 7, 2012 #1

    ElijahRockers

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Find the volume of the given solid.
    Under the plane x − 2y + z = 8 and above the region bounded by x + y = 1 and x2 + y = 1

    3. The attempt at a solution

    Here's how I set it up.

    [itex]\int^1_0 \int^{1-x^2}_{1-x} (8-x+2y) dydx[/itex]

    When I do the math, I get 21/20. I have gone several different routes using a calculator and I keep getting that answer. The software tells me the answer is 29/20.

    So am I setting it up wrong?
     
  2. jcsd
  3. Mar 7, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    For what it's worth, I get 21/20 as well.
     
  4. Mar 7, 2012 #3

    ElijahRockers

    User Avatar
    Gold Member

    Well, I copied and pasted the question directly from the software this time. Stupid software.
     
  5. Mar 7, 2012 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Well, assuming we are right, I doubt the software figured out the answer. Somebody told it what the answer should be. They are to blame.
     
  6. Mar 7, 2012 #5

    ElijahRockers

    User Avatar
    Gold Member

    Hmm I found an error in my work. The anti derivative of 8-x+2y is 8x-xy+y^2.

    I had 8x-xy-y^2.
     
  7. Mar 7, 2012 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think it's 8y-xy-y^2. Are you changing your answer? I'm not.
     
  8. Mar 7, 2012 #7

    ElijahRockers

    User Avatar
    Gold Member

    But if x-2y+z=8, then z=8-x+2y dz/dy = 8y -xy +y^2. I haven't gone through the problem, I did a similar one with different numbers and got it right
     
  9. Mar 7, 2012 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are integrating z, not differentiating it. I thought you did go through it and got 21/20?? I'm not sure where you are going with this. I think you did it right the first time.
     
  10. Mar 7, 2012 #9

    ElijahRockers

    User Avatar
    Gold Member

    Oh yeah, sorry, by dz/dy i mean the anti derivative.

    And yes, i got 21/20 when i used 8x-xy-y^2. I noticed my error, but by that time had already gotten the question right with a different set of values.

    I posted my error here just incase you were wondering, and to see if, by some bizarre one in a million coincidence, you made the same exact error I did. (not likely, especially considering you are probably much more careful than I am)
     
  11. Mar 7, 2012 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Wow. Apparently I'm not much more careful than you. I made a completely different error. I integrated z=8-x-2y instead of z=8-x+2y and got 21/20. Figured since I got the same as you did, no need to double check. Oooops. Yeah, the odds are pretty low for this to happen.
     
    Last edited: Mar 7, 2012
  12. Mar 7, 2012 #11

    ElijahRockers

    User Avatar
    Gold Member

    ........Actually, the odds drop drastically when we consider that you actually didn't make a completely different error, but you made the same exact error I did, completely separately from me. Look at the post where I mentioned my error.

    :surprised
     
  13. Mar 7, 2012 #12

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Ok, yeah. I get you, it's wasn't the 8x instead of the 8y, it was the sign on the 2y. That does cut the odds.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integration of multiple variables
Loading...