Results 1 to 2 of 2

Math Help - integrals, sin function and a denominator

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    91

    integrals, sin function and a denominator

    HI

    Okay the goal is to evaluate this integral

    integral sign (I will use S) (sin t^(1/2))/(t^1/2)

    so if I let u = t^1/2 and du = dt/2(t^1/2)

    S sin u / u du dt/du = I don't know what.

    If it was just sin u I would know that it = - cos u + C but I don't know what to do with the denominator.

    Please help me.

    Calculus beginner
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by calcbeg View Post
    HI

    Okay the goal is to evaluate this integral

    integral sign (I will use S) (sin t^(1/2))/(t^1/2)

    so if I let u = t^1/2 and du = dt/2(t^1/2)

    S sin u / u du dt/du = I don't know what.

    If it was just sin u I would know that it = - cos u + C but I don't know what to do with the denominator.

    Please help me.

    Calculus beginner
    \int\frac{\sin\sqrt{t}}{\sqrt{t}}\,dt

    You made a good choice for u but didn't sub it in correctly.

    u=\sqrt{t} and du=\frac{1}{2\sqrt{t}}\,dt

    Now the integral is 2\int\sin(u)\,du = -2\cos(u)+C=\boxed{-2\cos(\sqrt{t})+C}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrals leading to a Log function
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 4th 2011, 07:20 AM
  2. Replies: 9
    Last Post: January 21st 2011, 05:40 PM
  3. Limit of a function that has a common denominator
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: January 11th 2011, 11:45 AM
  4. Revenue Function - Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 21st 2010, 12:16 PM
  5. Length of a function using integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 25th 2006, 03:01 PM

Search Tags


/mathhelpforum @mathhelpforum