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Math Help - trig sub for a^2+u^2

  1. #1
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    trig sub for a^2+u^2

    <br />
\int\limits_{ - 2}^2 {\frac{{dx}}<br />
{{4 + x^2 }} = \int\limits_{\frac{{ - \pi }}<br />
{4}}^{\frac{\pi }<br />
{4}} {\frac{{2\sec ^2 u}}<br />
{{4\sec ^2 u}}du} } <br />

    My question is how do I go from 2,-2 to pi/4, -pi/4? Or, how do I get pi/4?

    Thanks.
    Last edited by kid funky fried; April 18th 2008 at 09:06 PM.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by kid funky fried View Post
    let me try this again.

    2 pi/4
    S dx/4+x^2 = S 2sec^2 u/4sec^2 u du
    -2 -pi/4


    How do I het pi/4, -pi/4 from 2, -2 ???

    Thanks.
    when you switch with substitution for definite integrals..you must evaluate your substitution with the limits of integration
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  3. #3
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    this does not help me. could you elaborate?
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  4. #4
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    Quote Originally Posted by kid funky fried View Post
    <br />
\int\limits_{ - 2}^2 {\frac{{dx}}<br />
{{4 + x^2 }} = \int\limits_{\frac{{ - \pi }}<br />
{4}}^{\frac{\pi }<br />
{4}} {\frac{{2\sec ^2 u}}<br />
{{4\sec ^2 u}}du} } <br />

    My question is how do I go from 2,-2 to pi/4, -pi/4? Or, how do I get pi/4?

    Thanks.
    You've made the substitution x = 2 \tan u.

    x = 2 \Rightarrow 2 = 2 \tan u \Rightarrow \tan u = 1 \Rightarrow u = \frac{\pi}{4}.

    x = -2 \Rightarrow -2 = 2 \tan u \Rightarrow \tan u = -1 \Rightarrow u = -\frac{\pi}{4}.
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    Thanks,
    I appreciate your help.
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