Results 1 to 5 of 5

Thread: How do I find this constant?

  1. #1
    Member billym's Avatar
    Joined
    Feb 2008
    Posts
    183

    How do I find this constant?

    $\displaystyle f(x,y)=\left\{
    \begin{array}{lr}
    cx^2+y& 0\le x\le 1,0\le y\le 1,y\le x\\
    0&elsewhere,
    \end{array}
    \right.$

    I can't figure out how to set this up. I have to show that c = 10, but every time I do it I get c = 5. What am I doing wrong:

    $\displaystyle 1=\int_{0}^{1}\int_{0}^{x}x^2y \, dydx=\frac{c}{5}\Longrightarrow c=5$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    you copied the density incorrectly, there is a + between the variables.

    $\displaystyle 1=\int_{0}^{1}\int_{0}^{x}\biggl(cx^2+y \biggr)\, dydx$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member billym's Avatar
    Joined
    Feb 2008
    Posts
    183
    Quote Originally Posted by billym View Post
    $\displaystyle f(x,y)=\left\{
    \begin{array}{lr}
    cx^2y& 0\le x\le 1,0\le y\le 1,y\le x\\
    0&elsewhere,
    \end{array}
    \right.$

    I can't figure out how to set this up. I have to show that c = 10, but every time I do it I get c = 5. What am I doing wrong:

    $\displaystyle 1=\int_{0}^{1}\int_{0}^{x}x^2y \, dydx=\frac{c}{5}\Longrightarrow c=5$
    Sorry, I actually wrote it down wrong the first time. The correct function is cx^2y. I still can't get ten out of it...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Focus's Avatar
    Joined
    Aug 2009
    Posts
    228
    Quote Originally Posted by billym View Post
    Sorry, I actually wrote it down wrong the first time. The correct function is cx^2y. I still can't get ten out of it...
    Thats because you computed the integral wrong.
    $\displaystyle
    \int_0^1 \int_0^x cx^2y \, dy dx=\int_0^1 \frac{1}{2}cx^2x^2 \, dx=\int_0^1 \frac{1}{2}cx^4\, dx=\frac{c}{10}
    $
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member billym's Avatar
    Joined
    Feb 2008
    Posts
    183
    was up too late. All makes perfect sense now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Oct 21st 2010, 12:24 PM
  2. To find the constant?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 19th 2009, 08:53 AM
  3. Find constant
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: Jun 4th 2009, 12:21 AM
  4. Find the value of the Constant
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Sep 22nd 2008, 08:29 AM
  5. Replies: 5
    Last Post: Feb 29th 2008, 02:05 PM

Search Tags


/mathhelpforum @mathhelpforum