Results 1 to 4 of 4

Thread: trigonometric integrals

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    91

    trigonometric integrals

    Hi the problem is to evaluate the following

    integral sign ("S") b=pi/3 a=0 sin^3 x dx

    so using the identity 1= sin^2 x + cos^2 x

    S sin^3 x dx = S sin x (1-cos^2 x) dx

    So if I let u= cos x du = sin x dx

    Then the original equation becomes = S (1-u^2) du
    = u - (1/3) u^3
    Substituting back and now applying a= 0 and b = pi/3
    = (cos pi/3 - (1/3) cos^3 pi/3) - (cos 0 - (1/3) cos^3 0)

    First am I doing this right?? And second if this is right does cos^3 pi/3 = 1/8?

    Thanks
    Calculus Beginner
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    15,073
    Thanks
    3169
    Quote Originally Posted by calcbeg View Post
    Hi the problem is to evaluate the following

    integral sign ("S") b=pi/3 a=0 sin^3 x dx

    so using the identity 1= sin^2 x + cos^2 x

    S sin^3 x dx = S sin x (1-cos^2 x) dx

    So if I let u= cos x du = sin x dx ... du = -sin x dx

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

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    91

    now regarding cos^3 pi/3

    is cos^3 pi/3 = (1/2)^3 = 1/8???

    Thanks

    Calculus Beginner
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    15,073
    Thanks
    3169
    Quote Originally Posted by calcbeg View Post
    is cos^3 pi/3 = (1/2)^3 = 1/8???

    Thanks

    Calculus Beginner
    yes
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Nov 14th 2009, 07:52 PM
  2. trigonometric integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 8th 2009, 10:32 PM
  3. trigonometric integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 4th 2009, 02:33 PM
  4. Trigonometric Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 22nd 2009, 04:14 AM
  5. Trigonometric Integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 23rd 2008, 04:08 PM

Search Tags


/mathhelpforum @mathhelpforum