Questão 04 Analise a integral dada abaixo int _(1)^infty x^2-3x+2dx Diante da integral acima analise as afirmativas a seguir 1. Trata-se de uma integral de Remann definida num intervalo infinito II. Seus limites de integração indicam um intervalo que cresce no infinito caracterizando-a como imprópria III. Seu resultado converge para 1 Estão corretas apenas as afirmativas

Vamos analisar a integral dada:<br /><br />\[<br />\int_{1}^{\infty} (x^2 - 3x + 2) \, dx<br />\]<br /><br />Primeiro, vamos verificar se as afirmativas são verdadeiras.<br /><br />### Afirmativa I:<br />"Trata-se de uma integral de Riemann definida num intervalo infinito."<br /><br />Isso é verdadeiro. A integral é definida no intervalo \([1, \infty)\), que é um intervalo infinito.<br /><br />### Afirmativa II:<br />"Seus limites de integração indicam um intervalo que cresce no infinito caracterizando-a como imprópria."<br /><br />Isso também é verdadeiro. Uma integral com um dos limites de integração sendo infinito é considerada uma integral imprópria.<br /><br />### Afirmativa III:<br />"Seu resultado converge para 1."<br /><br />Para verificar isso, precisamos calcular a integral. Vamos resolver a integral imprópria:<br /><br />\[<br />\int_{1}^{\infty} (x^2 - 3x + 2) \, dx<br />\]<br /><br />Primeiro, encontramos a antiderivada da função \(x^2 - 3x + 2\):<br /><br />\[<br />\int (x^2 - 3x + 2) \, dx = \frac{x^3}{3} - \frac{3x^2}{2} + 2x + C<br />\]<br /><br />Agora, aplicamos os limites de integração de 1 a \(\infty\):<br /><br />\[<br />\lim_{b \to \infty} \left[ \frac{x^3}{3} - \frac{3x^2}{2} + 2x \right]_{1}^{b}<br />\]<br /><br />Calculamos a expressão nos limites:<br /><br />\[<br />\lim_{b \to \infty} \left( \left[ \frac{b^3}{3} - \frac{3b^2}{2} + 2b \right] - \left[ \frac{1^3}{3} - \frac{3 \cdot 1^2}{2} + 2 \cdot 1 \right] \right)<br />\]<br /><br />Simplificando o termo constante:<br /><br />\[<br />\frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} + \frac{3}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6} = \frac{1}{3} - \frac{3}{2} + 2 = \frac{1}{3} - \frac{9}{6} + \frac{12}{6