Results 1 to 10 of 10

Math Help - Area between curves

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    22

    Thumbs up Area between curves

    Hey all!


    I have this problem, and am unable to comprehend what to do, I haven't stumbled upon a question like this before. If anyone can offer assistance, it would be much appreciated.



    Consider the two curves y = 4/x and y = -x+5
    (a) Calculate the area enclosed by the two curves.
    (b) Find the volume of the solid generated by rotating the region about the y-axis.


    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2009
    Posts
    22
    For: Part (a) Calculate the area enclosed by the two curves:

    I got the answer: (13/2)-4ln|4|, is this correct?

    How about Part (b), how do I go about that question?

    Thanks again.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,598
    Thanks
    1421
    No, it is not. Since you did not show your work, I cannot say any more than that.

    As for the volume formed by rotating the region, there are many ways of doing that. What methods do you know?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2009
    Posts
    22
    I used the formula: A = \int_1^4 Yt - Yb dx

    A = \int_1^4 (-x+5) - (4/x) dx

    Have I perhaps placed the functions incorrectly, using this formula?

    Following through:
    [(-(x^2)/2 + 5x - 4ln|x|]_1^4

    [(-((4)^2)/2 + 5(4) - 4ln|(4)|] - [(-((1)^2)/2 + 5(1) - 4ln|1|]

    [-8 + 20 - 4ln|(4)|] - [1/2 + 5 - 0]

    12 - 4ln|(4)| - 11/2

    Finally giving the result:
    13/2 - 4ln|4|

    Where did I go wrong?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2009
    Posts
    3

    area between curves

    looks like you used a valid method. Below is part of your working ....





    note the 1/2 in the last bracket must be negative. That way, the answer becomes 15/2 - ln16.

    For the second part you may

    use pie*int[f(x)-g(x)]^2]dx
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2009
    Posts
    3

    area between curves

    the answer is actually 15/2-ln256
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2009
    Posts
    22
    Where did you get 15/2 from? Shouldn't it be 35/2? ( 12 + 11/2 = 35/2)

    -> Giving the result: (35/2)-ln|256|?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430
    Quote Originally Posted by iExcavate View Post
    Where did you get 15/2 from? Shouldn't it be 35/2? ( 12 + 11/2 = 35/2)
    -> Giving the result: (35/2)-ln|256|?
    ...
    Last edited by skeeter; October 16th 2009 at 06:15 PM. Reason: fix error
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Oct 2009
    Posts
    22
    11/2 = 5.5

    12 - 11/2 = 13/2 (what I initially had)
    12 - 5.5 = 6.5 -> 13/2


    Where did 15/2 come from?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430
    picking it up from scratch ...

    \left[-\frac{x^2}{2} + 5x - 4\ln{x}\right]_1^4

    \left[-8 + 20 - 4\ln{4}\right] - \left[-\frac{1}{2} + 5 - 4\ln{1}\right]

    12 - 4\ln{4} - \frac{9}{2} = \frac{15}{2} - 8\ln{2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area between Curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 15th 2011, 03:24 PM
  2. Area between two curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 11th 2010, 09:52 PM
  3. area between curves.
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 11th 2010, 11:39 AM
  4. Area Between Two Curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 10th 2009, 03:15 PM
  5. Area between two curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 27th 2009, 04:59 PM

Search Tags


/mathhelpforum @mathhelpforum