Question

Según el ejercicio seleccionado, desarrollar la integral impropia.

Answer 1

$\displaystyle\\I=\int_{-\infty}^{0}\dfrac{4}{4+x^2}dx=\int_{-\infty}^{0}\dfrac{1}{1+(\frac{x}{2})^2}dx\\ \\ \\I=2\int_{-\infty}^{0}\dfrac{1}{1+x^2}dx=2\left\arctan x\right|_{-\infty}^{0}\\ \\\\I=2[0-(-\dfrac{\pi}{2})] \\ \\ \\\boxed{\int_{-\infty}^{0}\dfrac{4}{4+x^2}dx=\pi}$