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Math Help - Trigonometric Substitution Question

  1. #1
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    Trigonometric Substitution Question

    Hello,

    I am absolutely stumped on this one.



    I'm assuming all of my work is correct up until the end, but I don't know how to proceed using Trigonometric Substitution. Please help!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Troopa View Post
    Hello,

    I am absolutely stumped on this one.



    I'm assuming all of my work is correct up until the end, but I don't know how to proceed using Trigonometric Substitution. Please help!
    \frac 1{\sec^2 \theta} = \cos^2 \theta = \frac 12 (1 + \cos 2 \theta)

    (and of course it's not \frac 1{\tan \theta + C} there is no integration rule to justify such a step!)
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  3. #3
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    So then...

    = \frac 12 (1 + \cos 2 \theta)

    = \frac 12 (\theta + (cos2 \theta^2 / 2))

    Is this right?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Troopa View Post
    So then...

    = \frac 12 (1 + \cos 2 \theta)

    = \frac 12 (\theta + (cos2 \theta^2 / 2))

    Is this right?
    no.

    first, where's your integral sign?

    secondly, how do we integrate cosine? We don't just simply integrate the argument.
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  5. #5
    No one in Particular VonNemo19's Avatar
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    \int\frac{1}{\sec^2\theta}d\theta=\int\cos^2\theta  {d}\theta=\frac{1}{2}\int(1+\cos2\theta)d\theta=\f  rac{1}{2}(\theta+\frac{1}{2}\sin{2\theta})+C

    Now back substitute.
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  6. #6
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    Thanks for your help. I'm gonna finish this and get some help in my math lab.
    Last edited by Troopa; January 21st 2010 at 09:27 PM.
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