Results 1 to 4 of 4

Math Help - Area under the curve of sin(x)

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    8

    Area under the curve of sin(x)

    Hi,
    Please could someone help with the following problem.

    (a) Sketch the curve for y = sin(x) between x = 0 and x = 2pi,

    (b) Then find the total area enclosed by the curve y = sin x and the X axis between
    x = 0 and x = 1.7pi

    I've sketched the curve but I'm struggling with the second part, please see below.



    Next I integrated the area above the X axis using the limits.



    Then I integrated the area below the X axis using the limits.



    When I subtract area1 from area2 i seem to be getting an answer of 0, which doesn't seem right.
    Any help appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie Esteban's Avatar
    Joined
    Feb 2013
    From
    Santiago, Chile
    Posts
    16
    Thanks
    3

    Re: Area under the curve of sin(x)

    Remember sinus function is periodic, with an specific period. Then, the area under the fuction in the first interval wich it's positive, it's the same area in the second interval wich is negative. (Try to draw it to see)

    Then, when you're trying to calculate the area yo have to take the following integral:

    A=\displaystyle \int_{a}^{b}\left |f(x)  \right |dx

    a,b you have to choose it propperly to get the correct answer
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2011
    Posts
    8

    Re: Area under the curve of sin(x)

    Maybe I'm getting confused but the area in the second interval will be smaller than the first because the original curve is sin(x) between x=0 and x=2pi. The area I have to find is sin(x) between x=0 and x=1.7pi. To find the total area enclosed I thought I would have to subtract one from the other.

    I have drawn the sinewave using the following
    0 time=0 degrees
    pi/2(t)=90 degrees
    pi(t)=180 degrees
    3pi/2=270 degrees
    2pi=360 degrees
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: Area under the curve of sin(x)

    Quote Originally Posted by chrisn30 View Post
    Maybe I'm getting confused but the area in the second interval will be smaller than the first because the original curve is sin(x) between x=0 and x=2pi. The area I have to find is sin(x) between x=0 and x=1.7pi. To find the total area enclosed I thought I would have to subtract one from the other.

    Please, please stop using degrees. It is so out-of-date.

    You want: \int_0^\pi  {\sin (x)dx}  + \int_\pi ^{1.7\pi } { - \sin (x)dx}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area between a curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 13th 2012, 11:00 AM
  2. Area Under a Curve
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 3rd 2009, 12:11 AM
  3. Area between the curve?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 12th 2009, 03:19 AM
  4. area under the curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 24th 2008, 06:32 AM
  5. Curve area
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: January 24th 2008, 04:40 AM

Search Tags


/mathhelpforum @mathhelpforum