Results 1 to 5 of 5

Math Help - Definite Integration

  1. #1
    Banned
    Joined
    Dec 2008
    Posts
    67

    Definite Integration

    Evaluate
    \int\limits_{-1}^{1}\frac{3+sin^3 x}{1+x^2}dx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by varunnayudu View Post
    Evaluate
    \int\limits_{-1}^{1}\frac{3 - sin^3 x}{1+x^2}dx
    Note that \int\limits_{-1}^{1}\frac{\sin^3 x}{1+x^2} \, dx = 0 since \sin^3 x is an odd function.

    So \int\limits_{-1}^{1}\frac{3 - \sin^3 x}{1+x^2} \, dx = \int\limits_{-1}^{1}\frac{3}{1+x^2} \, dx which you should be able to easily do.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Dec 2008
    Posts
    67

    hw did u get this

    Quote Originally Posted by mr fantastic View Post
    Note that \int\limits_{-1}^{1}\frac{\sin^3 x}{1+x^2} \, dx = 0 since \sin^3 x is an odd function.

    So \int\limits_{-1}^{1}\frac{3 - \sin^3 x}{1+x^2} \, dx = \int\limits_{-1}^{1}\frac{3}{1+x^2} \, dx which you should be able to easily do.

    ------------------------------------------------------------------

    hw did u get

    <br />
 \frac{sin^3x}{1+x} = 0.<br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,392
    Thanks
    55
    Quote Originally Posted by varunnayudu View Post
    ------------------------------------------------------------------

    hw did u get

    <br />
\frac{sin^3x}{1+x} = 0.<br />
    He didn't say

    <br />
\frac{sin^3x}{1+x^2} = 0. (note the number 2)

    He said that

    <br />
\int_{-1}^1 \frac{sin^3x}{1+x^2}\, dx = 0.<br />

    In fact, if  f(x) is odd and continuous on [-a,a] then

     \int_{-a}^a f(x) \, dx = 0.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    If you're not convinced, substitute t=-x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: September 2nd 2010, 01:27 PM
  2. Definite Integration
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 10th 2010, 06:31 PM
  3. Definite integration help.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 7th 2009, 12:06 PM
  4. Integration, definite
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 6th 2008, 10:12 PM
  5. Definite Integration
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 9th 2007, 04:49 AM

Search Tags


/mathhelpforum @mathhelpforum