Results 1 to 4 of 4

Math Help - Integrals: Arc Length and hydrostatic force problem

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    32

    Integrals: Arc Length and hydrostatic force problem

    Alright my first is to simply find the length of the curve of:

    y = ln(sec x) from 0 to pi/4

    the steps I have taken is the usual dy/dx = tan x

    then

    integral of sqrt(1 + (tan x)^2)

    from here is where I am stuck. I've tried using u-substitution but then du would've been more complicated to calculate out and I don't know how to integrate the expression sqrt(1 + (tan x)^2). what should I proceed with?


    my next problem is: a swimming pool 20ft wide, 40ft long, bottom is an inclined plane. shallow end is 3 ft long, deep end is 9ft long and pool is full of water. find hydrostatic force on one of the sides.

    I started by drawing a picture of said pool then I made a plane with the x axes with origin at top of pool going down
    then i make a strip of \Delta x.

    this is where I am stuck as I am not sure as to which side I should be working towards finding pressure of (if it matters).

    how should I proceed with this one? I'm looking at a few other answers and I'm guessing I should find the area of the strip, if so, how to properly do this? cause at some points the strip would be a rectangle but at some it'd be a triangle.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by deltemis View Post
    Alright my first is to simply find the length of the curve of:

    y = ln(sec x) from 0 to pi/4

    the steps I have taken is the usual dy/dx = tan x

    then

    integral of sqrt(1 + (tan x)^2)

    from here is where I am stuck. I've tried using u-substitution but then du would've been more complicated to calculate out and I don't know how to integrate the expression sqrt(1 + (tan x)^2). what should I proceed with?


    [snip]
    Know your identities: 1 + \tan^2 x = \sec^2 x.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,319
    Thanks
    1241
    Quote Originally Posted by deltemis View Post
    Alright my first is to simply find the length of the curve of:

    y = ln(sec x) from 0 to pi/4

    the steps I have taken is the usual dy/dx = tan x

    then

    integral of sqrt(1 + (tan x)^2)

    from here is where I am stuck. I've tried using u-substitution but then du would've been more complicated to calculate out and I don't know how to integrate the expression sqrt(1 + (tan x)^2). what should I proceed with?


    my next problem is: a swimming pool 20ft wide, 40ft long, bottom is an inclined plane. shallow end is 3 ft long, deep end is 9ft long and pool is full of water. find hydrostatic force on one of the sides.

    I started by drawing a picture of said pool then I made a plane with the x axes with origin at top of pool going down
    then i make a strip of \Delta x.

    this is where I am stuck as I am not sure as to which side I should be working towards finding pressure of (if it matters).

    how should I proceed with this one? I'm looking at a few other answers and I'm guessing I should find the area of the strip, if so, how to properly do this? cause at some points the strip would be a rectangle but at some it'd be a triangle.
    1 + \tan^2{x} = \sec^2{x}

    so

    \sqrt{1 + \tan^2{x}} = \sec{x}.


    So the arc length is \int{\sec{x}\,dx}.

    Can you go from here?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2009
    Posts
    32
    ah forgot about that identity, yep got that first one solved

    not sure about that second problem
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Need help setting up hydrostatic force problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 20th 2011, 06:30 AM
  2. hydrostatic force problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 5th 2009, 10:28 AM
  3. word problem for hydrostatic force
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 24th 2009, 09:31 AM
  4. Hydrostatic Force Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 24th 2009, 03:30 AM
  5. Hydrostatic Force Problem!!!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 23rd 2008, 06:01 PM

Search Tags


/mathhelpforum @mathhelpforum