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: Surface Area

  1. Mar 24, 2007 #1
    1. The problem statement, all variables and given/known data
    [tex]S={(x,y,z): z=x+y^2, 0\leq x\leq1 , x\leq y \leq 1 [/tex]

    2. Relevant equations
    A=a(S) = [tex]$
    \int\int_R \sqrt{(1+(\frac{\partial f}{\partial x})^2 + (\frac{\partial f}{\partial y})^2\,dy\,dx[/tex]

    3. The attempt at a solution
    [tex]S={(x,y,z): z=x+y^2, 0\leq x\leq1 , x\leq y \leq 1 [/tex]

    I suppose I can write this as:

    [tex]S={(x,y,z): z=x+y^2, y\leq x\leq1 , 0\leq y \leq 1 [/tex]
    And so i think:

    A=a(S) = [tex]$
    \int_0^1\int_y^1 \sqrt{2+4y^2}\,dy\,dx[/tex]

    If I calculate this I don't get the answer that I should..
    Last edited: Mar 24, 2007
  2. jcsd
  3. Mar 24, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    It would help a great deal to know what you got and how you got it.
  4. Mar 24, 2007 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    SKETCH the region given!!

    Do it in the following way:

    1. Draw the rectangle strip [tex]0\leq{x}\leq{1}[/tex] in the xy-plane.
    2. Since y<=1, draw the line y=1. You are to be below this line, within the strip from 1.

    3. Now, you have x<=y. Draw the line x=y, you are to be above that line.

    4. Thus, you may represent the region as follows:
    [tex]0\leq{x}\leq{1}, x\leq{y}\leq{1}[/tex]
    These limits on y were gained by looking at the vertical line segments the region consists of for all x-positions of these segments from 0 to 1.

    Alternatively, we may consider the horizontal line segments the region consists of; this yields the equally valid representation:
    [tex]0\leq{y}\leq{1}, 0\leq{x}\leq{y}[/tex]

    These are the two simplest correct region representations, yours is not correct.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook