Results 1 to 9 of 9
Like Tree6Likes
  • 2 Post By 1729
  • 1 Post By 1729
  • 2 Post By integral95
  • 1 Post By dan964

Thread: integration area of sinx and cos x

  1. #1
    Cadet
    Join Date
    Jan 2016
    HSC
    2018
    Gender
    Male
    Posts
    42
    Rep Power
    2

    integration area of sinx and cos x

    So, How does one find the total shaded area (red and green in the attachment).
    I'm unsure whether the first half (red part) is going to be the integral of sinx or (cosx -sinx)

    My instinct working out for total area of the shaded:

    integration of sin x between 0 and 45 + [integration of sinx -cos x in between 45 to 90]
    Attached Images Attached Images

  2. #2
    Junior Member 1729's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Location
    Sydney
    Posts
    118
    Rep Power
    1

    Re: integration area of sinx and cos x

    Quote Originally Posted by cloud edwards View Post
    So, How does one find the total shaded area (red and green in the attachment).
    I'm unsure whether the first half (red part) is going to be the integral of sinx or (cosx -sinx)

    My instinct working out for total area of the shaded:

    integration of sin x between 0 and 45 + [integration of sinx -cos x in between 45 to 90]
    Last edited by 1729; 22 Jun 2017 at 1:20 AM. Reason: Integral bounds

  3. #3
    Cadet
    Join Date
    Jan 2016
    HSC
    2018
    Gender
    Male
    Posts
    42
    Rep Power
    2

    Re: integration area of sinx and cos x

    Ok thanx, so how did u get the second half (i.e. cosx)

  4. #4
    Junior Member 1729's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Location
    Sydney
    Posts
    118
    Rep Power
    1

    Re: integration area of sinx and cos x

    Quote Originally Posted by cloud edwards View Post
    Ok thanx, so how did u get the second half (i.e. cosx)
    Last edited by 1729; 22 Jun 2017 at 1:18 AM.
    cloud edwards likes this.

  5. #5
    Cadet
    Join Date
    Jan 2016
    HSC
    2018
    Gender
    Male
    Posts
    42
    Rep Power
    2

    Re: integration area of sinx and cos x

    Thanx bro, you're a lifesaver!

  6. #6
    Senior Member integral95's Avatar
    Join Date
    Dec 2012
    HSC
    2013
    Gender
    Male
    Posts
    658
    Rep Power
    4

    Re: integration area of sinx and cos x

    Going to be a bit pedantic here, but you shouldn't be using your limits in terms of degree but in radians, it could create a lot of awkward scaling factors especially if you're combining trig functions with some linear function.

    e.g

    wouldn't give you the right value for the area under the curve.
    4025808 and cloud edwards like this.
    “Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
    ― Brandon Mull

  7. #7
    Cadet
    Join Date
    Jan 2016
    HSC
    2018
    Gender
    Male
    Posts
    42
    Rep Power
    2

    Re: integration area of sinx and cos x

    How different would it be if i didn't use radians, i'm a bit confused with the example,
    sorry.

  8. #8
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,339
    Rep Power
    4

    Re: integration area of sinx and cos x

    Quote Originally Posted by cloud edwards View Post
    How different would it be if i didn't use radians, i'm a bit confused with the example,
    sorry.
    It is how the derivative of cos x and sin x is defined. We use radians instead of degrees as the computation is simpler.
    for x in degrees
    cloud edwards likes this.
    2014 HSC
    2015 Gap Year
    2016-2018 UOW Bachelor of Maths/Maths Advanced.

    Links:
    View English Notes (no download)
    Maths Notes - Free Sample

  9. #9
    Cadet
    Join Date
    Jan 2016
    HSC
    2018
    Gender
    Male
    Posts
    42
    Rep Power
    2

    Re: integration area of sinx and cos x

    Ok sweet, thanx guys

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •