Calculadora de integrales definidas e impropias

La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.

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Integrate with respect to:

Enter a lower limit:

If you need `-oo`, type -inf.

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

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Solution

Your input: calculate $$$\int_{0}^{t}\left( \frac{1}{t} \right)dt$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{1}{t} d t}=\ln{\left(\left|{t}\right| \right)}$$$ (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.

$$$\left(\ln{\left(\left|{t}\right| \right)}\right)|_{\left(t=t\right)}=\ln{\left(\left|{t}\right| \right)}$$$

$$$\left(\ln{\left(\left|{t}\right| \right)}\right)|_{\left(t=0\right)}=-\infty$$$

$$$\int_{0}^{t}\left( \frac{1}{t} \right)dt=\left(\ln{\left(\left|{t}\right| \right)}\right)|_{\left(t=t\right)}-\left(\ln{\left(\left|{t}\right| \right)}\right)|_{\left(t=0\right)}=\ln{\left(\left|{t}\right| \right)} + \infty$$$

Answer: $$$\int_{0}^{t}\left( \frac{1}{t} \right)dt=\ln{\left(\left|{t}\right| \right)} + \infty$$$

Calculadora de integrales definidas e impropias

Calcular integrales definidas e impropias paso a paso

Solution