Results 1 to 3 of 3

Math Help - [SOLVED] Trig Substitution Integral

  1. #1
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1

    [SOLVED] Trig Substitution Integral

    Integrate.

    \int \frac{3}{x^2\sqrt{100-sin x^2}} dx

    Here is what I have done (I left out all my early steps):

    \int \frac{30 cos\theta d\theta}{(10sin\theta)^2 (\sqrt{100-sin ^2\theta)}}

    <br />
\int \frac{30 cos\theta d\theta}{100(sin^2\theta) \cdot (10\sqrt{1-sin ^2 \theta}}

    <br />
\int \frac{30 cos\theta d\theta}{1000sin^2\theta \sqrt{cos ^2 \theta}}

    = \frac{30}{1000} \int \frac{1}{sin^2 \theta} d\theta

    <br />
= \frac{30}{1000} \int \frac{2}{1-cos(2\theta)} d\theta

    Can someone please check this for me? Should I do a u sub with 2\theta? Thanks!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    I think you went one line too far. \frac{1}{\sin^2(x)} = \csc^2(x), which is an easy integral.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2008
    Posts
    792
    Just to make sure, I will assume that you meant
    \int \frac{3}{x^2\sqrt{100-x^2}}~dx

    In your second step, you probably forgot to write 100\sin^2{\theta}.

    In your last step, you applied a trig identity in a wrong way. \frac{1}{\sin^2{x}} is a standard form. If it helps, \frac{1}{\sin^2{x}} = \csc^2{x}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Trig Substitution Integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 20th 2009, 08:56 PM
  2. Replies: 3
    Last Post: April 5th 2009, 10:14 AM
  3. [SOLVED] trig substitution integral
    Posted in the Calculus Forum
    Replies: 12
    Last Post: February 11th 2009, 09:15 PM
  4. [SOLVED] Using both u and trig substitution
    Posted in the Calculus Forum
    Replies: 14
    Last Post: September 8th 2008, 01:42 PM
  5. [SOLVED] Trig substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 8th 2008, 09:32 AM

Search Tags


/mathhelpforum @mathhelpforum