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: Find n for the shaded region

  1. May 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the value of n so that the area of the shaded region (refer to attached picture) in the following diagram is a) 50% of the area of the unit square b) 80% of the area of the unit square

    2. Relevant equations
    Definate integral properities, fundamental theorem of calculus

    3. The attempt at a solution
    My teacher says this is an easy question, but I cannot seem to solve it. My first guess was to take the integral of the two functions and then use the percentages as the answers for the integral, solving for n in each case (in this case I made 50% = 1/2 and 80% = 4/5). This did not get me very far for I came up with square roots and fractions in my answers when they should be simply be one number answers. Am I doing this question right through this method, or is this the wrong procedure and do I need to do something different to find the correct answers? Any help would be very welcome, thanks in advance. PS: sorry for the bad picture :tongue:

    Attached Files:

  2. jcsd
  3. May 17, 2009 #2


    Staff: Mentor

    The picture has been pending approval for several hours. Can you describe the region in words?
  4. May 17, 2009 #3
    There are two functions, y = x^n and y = x^1/n located in region I of the graph. The area to be found is the area in-between these two functions, and runs from their point of intersection at (0,0) to the other point at (1,1). y = x^n is located below y = x^1/n (though i'm sure you probably already figured that out :tongue:).
  5. May 17, 2009 #4
    [tex]A=\int_0^1\int_{x^n}^{x^{1/n}} dydx[/tex]
    (depending if n>1 or n<1)

    Evaluate the integral then solve for n. I get:

    Last edited: May 17, 2009
  6. May 17, 2009 #5
    I understand the last part, but I don't know how to get (n-1)/(n+1) from that integral you used. Unless you mean finding the integral of x^1/n - x^n over [0,1]?
  7. May 18, 2009 #6
    Hi. Didn't notice you replied until now.

    << solution deleted by berkeman >>
    Last edited by a moderator: May 18, 2009
  8. May 18, 2009 #7
    Thanks squidsoft, I managed to solve that one.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook