Belirli ve Uygunsuz İntegral Hesaplayıcı

Hesaplayıcı, uygunsuz olanlar da dahil olmak üzere belirli (yani sınırları olan) integrali adımları göstererek hesaplamaya çalışacaktır.

Enter a function:

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 $$$\int_{0}^{1}\left( \frac{1}{x} \right)dx$$$

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

The interval of integration contains the point $$$0$$$, which is not in the domain of the integrand, so this is an improper integral of type 2.

To evaluate an integral over an interval, we use the Fundamental Theorem of Calculus. However, we need to use limit if an endpoint of the interval is special (is not in the domain of the function).

$$$\int_{0}^{1}\left( \frac{1}{x} \right)dx=\left(\ln{\left(\left|{x}\right| \right)}\right)|_{\left(x=1\right)}-\lim_{x \to 0}\left(\ln{\left(\left|{x}\right| \right)}\right)=\infty$$$

Since the value of the integral is not finite, then it is divergent.

Answer: the integral is divergent.

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Belirli ve Uygunsuz İntegral Hesaplayıcı

Belirli ve uygunsuz integralleri adım adım hesaplayın

Solution