Math Help - convergent integral

1. convergent integral

so im pretty sure its convergent but the answer i get is arctan(6) anyone know what im doing wrong.

2. Originally Posted by dat1611

so im pretty sure its convergent but the answer i get is arctan(6) anyone know what im doing wrong.
$\int\limits_{ - \infty }^6 {\frac{{dx}}{{{x^2} + 1}}} = \left. {\arctan x} \right|_{ - \infty }^6 = \arctan 6 - \underbrace {\mathop {\lim }\limits_{x \to - \infty } \arctan x}_{ - \pi /2} = \arctan 6 + \frac{\pi }{2}.$

3. Originally Posted by dat1611

so im pretty sure its convergent but the answer i get is arctan(6) anyone know what im doing wrong.
the integral is convergent ...

$\lim_{a \to -\infty} \int_a^6 \frac{1}{x^2+1} \, dx$

$\lim_{a \to -\infty} \left[\arctan{x}\right]_a^6$

$\lim_{a \to -\infty} \left[\arctan(6) - \arctan{a}\right] = \arctan(6) - \left(-\frac{\pi}{2}\right) = \arctan(6) + \frac{\pi}{2}$