Results 1 to 4 of 4

Math Help - Volume of revolution

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    77

    Volume of revolution

    The area between the curve y=sin2x, the x-axis between 0 and 1 and the line x=1 is rotated through 360 degrees about the x-axis.

    a) Sketch the area described.
    b) Write down an integral expression for the volume of the solid formed.
    c) Find this volume.

    That's the whole question, I provided a,b, and c for completeness. What I need some explanation on is with regards to the line x=1.
    I drew 2 functions on the same set of axes: y=sin (x+pi/4) and x=1...
    Is that right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member eddie2042's Avatar
    Joined
    Apr 2010
    Posts
    70
    Thanks
    1
    Quote Originally Posted by bhuang View Post
    The area between the curve y=sin2x, the x-axis between 0 and 1 and the line x=1 is rotated through 360 degrees about the x-axis.

    a) Sketch the area described.
    b) Write down an integral expression for the volume of the solid formed.
    c) Find this volume.

    That's the whole question, I provided a,b, and c for completeness. What I need some explanation on is with regards to the line x=1.
    I drew 2 functions on the same set of axes: y=sin (x+pi/4) and x=1...
    Is that right?
    Um.. no. I think the x = 1 is just there to enclose the area.

    The question is worded crappy. It should be:

    Consider the area in the first quadrant bounded by y = sin (2x) and x = 1.

    Less confusion..

    Whats your answer? I got

    V = -\frac{1}{4}\pi cos(2)sin(2) + \frac{\pi}{2} \approx 1.86799
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    77
    Well, then there is still two equations: y=something and x=something, so how am I supposed to work that out?

    The answer in the book only works out the solution with the y=sin2x equation, which I am able to work out
    However, I don't understand the x=1. If it still bounds the area, then isn't it still one of the equations....?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member eddie2042's Avatar
    Joined
    Apr 2010
    Posts
    70
    Thanks
    1
    Quote Originally Posted by bhuang View Post
    Well, then there is still two equations: y=something and x=something, so how am I supposed to work that out?

    The answer in the book only works out the solution with the y=sin2x equation, which I am able to work out
    However, I don't understand the x=1. If it still bounds the area, then isn't it still one of the equations....?

    No it's not. It's just put there so that you know that your limits of integration will be from 0 to 1 but you only use the y = sin(2x).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. volume of revolution
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: April 13th 2011, 05:53 AM
  2. Volume of Revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 16th 2009, 04:44 PM
  3. Volume of revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2009, 06:37 PM
  4. Volume by revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2009, 03:37 PM
  5. Volume of revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 22nd 2008, 11:09 AM

Search Tags


/mathhelpforum @mathhelpforum