Calculadora de integrales definidas e impropias
Calcular integrales definidas e impropias paso a paso
La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.
Solution
Your input: calculate $$$\int_{0}^{n}\left( \frac{1}{x^{2}} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{\frac{1}{x^{2}} d x}=- \frac{1}{x}$$$ (for steps, see indefinite integral calculator)
According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.
$$$\left(- \frac{1}{x}\right)|_{\left(x=n\right)}=- \frac{1}{n}$$$
$$$\left(- \frac{1}{x}\right)|_{\left(x=0\right)}=-\infty$$$
$$$\int_{0}^{n}\left( \frac{1}{x^{2}} \right)dx=\left(- \frac{1}{x}\right)|_{\left(x=n\right)}-\left(- \frac{1}{x}\right)|_{\left(x=0\right)}=\infty - \frac{1}{n}$$$
Answer: $$$\int_{0}^{n}\left( \frac{1}{x^{2}} \right)dx=\infty - \frac{1}{n}$$$