Question

O cálculo da integral resulta em 2 a -infinito dxsobre4-xao quadrado

Answer 1

$\displaystyle I=\int_2^{-\infty}\frac{dx}{4-x^2}\\ \\ I=\frac{1}{4}\int_2^{-\infty}\frac{1}{2-x}+\frac{1}{2+x}\,dx\\ \\ I=\frac{1}{4}\left.\left(\ln\left|\frac{2+x}{2-x}\right|\right)\right|_2^{-\infty}\\ \\ I=\frac{1}{4}\left(\lim\limits_{x\to -\infty}\ln\left|\frac{2+x}{2-x}\right|-\lim\limits_{x\to 2}\ln\left|\frac{2+x}{2-x}\right|\right)\\ \\ I=\frac{1}{4}(0-\infty)\\ \\ I=-\infty$