Desarrollar las siguientes integrales impropias

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Hola flover!

$$\begin{align}&A(t)=\int_1^t x^{-3}dx=\frac{x^{-2}}{-2}=-\frac{1}{2x^2} \Bigg |_1^t=-\frac 1 2 \Big(\frac  1 {t^2}-1\Big)= \frac{1}{2} \Big(1-\frac{1}{t^2} \Big)\\&\\&A(10)=\frac{1}{2} \Big(1-\frac{1}{10^2} \Big)=0.495\\&\\&A(100)=\frac{1}{2} \Big(1-\frac{1}{100^2} \Big)=0.49995\\&\\&A(1000)=\frac{1}{2} \Big(1-\frac{1}{1000^2} \Big)=0.4999995\\&\\&A=\int_1^{\infty} x^{-3}dx= \frac{1}{2} \Big(1-\frac{1}{\infty} \Big)=\frac{1}{2}(1-0)=0.5\end{align}$$

saludos

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