Analise as integrais impróprias a seguir, indicando a não convergência ou calculando-as, caso contrário: 1.1 ∫ +∞ 1 1 x2 dx ; 1.2 ∫ +∞ 2 1 x2...

Vamos analisar cada uma das integrais: 1.1 ∫ +∞ 1 1/x^2 dx: Essa integral converge, pois a função integranda é decrescente e positiva no intervalo de integração. Podemos calcular o valor da integral: ∫ +∞ 1 1/x^2 dx = [-1/x] +∞ 1 = 1 - 0 = 1. 1.2 ∫ +∞ 2 (1/x^2 - 1) dx: Essa integral também converge, pois a função integranda é decrescente e positiva no intervalo de integração. Podemos calcular o valor da integral: ∫ +∞ 2 (1/x^2 - 1) dx = ∫ +∞ 2 (1/x^2) dx - ∫ +∞ 2 dx = [-1/x] +∞ 2 - [x] +∞ 2 = (0 - (-1/2)) - (∞ - 2) = 1/2 + 2 = 5/2. 1.3 ∫ +∞ -∞ 1/(9 + x^2) dx: Essa integral converge, pois a função integranda é decrescente e positiva no intervalo de integração. Podemos calcular o valor da integral utilizando a técnica de substituição trigonométrica: ∫ +∞ -∞ 1/(9 + x^2) dx = ∫ +∞ -∞ 1/(3^2 + (x/3)^2) dx Fazendo a substituição x/3 = tan(t), temos dx = 3sec^2(t) dt e a integral se torna: ∫ +∞ -∞ 1/(3^2 + (x/3)^2) dx = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^2(t) dt = ∫ +∞ -∞ 1/(3^2 + tan^2(t)) * 3sec^