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

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

$
\int\limits_{ - 2}^2 {\frac{{dx}}
{{4 + x^2 }} = \int\limits_{\frac{{ - \pi }}
{4}}^{\frac{\pi }
{4}} {\frac{{2\sec ^2 u}}
{{4\sec ^2 u}}du} }
$

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

Thanks.

2. Originally Posted by kid funky fried
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

3. this does not help me. could you elaborate?

4. Originally Posted by kid funky fried
$
\int\limits_{ - 2}^2 {\frac{{dx}}
{{4 + x^2 }} = \int\limits_{\frac{{ - \pi }}
{4}}^{\frac{\pi }
{4}} {\frac{{2\sec ^2 u}}
{{4\sec ^2 u}}du} }
$

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 $x = 2 \tan u$.

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

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

5. Thanks,