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.

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Solution

Your input: calculate $$$\int_{1}^{2}\left( \frac{1}{x} \right)dx$$$

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

$$$\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=2\right)}=\ln{\left(2 \right)}$$$

$$$\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=1\right)}=0$$$

$$$\int_{1}^{2}\left( \frac{1}{x} \right)dx=\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=2\right)}-\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=1\right)}=\ln{\left(2 \right)}$$$

Answer: $$$\int_{1}^{2}\left( \frac{1}{x} \right)dx=\ln{\left(2 \right)}\approx 0.693147180559945$$$

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Calculadora de integrales definidas e impropias

Calcular integrales definidas e impropias paso a paso

Solution