Kalkulator Integral Tentu dan Tak Wajar

Kalkulator akan mencoba mengevaluasi integral tentu (yaitu dengan batas-batas), termasuk integral tak wajar, dengan menampilkan langkah-langkahnya.

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Integrate with respect to:

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

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If you need `oo`, type inf.

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Solution

Your input: calculate $$$\int_{1}^{19}\left( \frac{\ln{\left(x \right)}}{x^{3}} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{\ln{\left(x \right)}}{x^{3}} d x}=\frac{- 2 \ln{\left(x \right)} - 1}{4 x^{2}}$$$ (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.

$$$\left(\frac{- 2 \ln{\left(x \right)} - 1}{4 x^{2}}\right)|_{\left(x=19\right)}=- \frac{\ln{\left(19 \right)}}{722} - \frac{1}{1444}$$$

$$$\left(\frac{- 2 \ln{\left(x \right)} - 1}{4 x^{2}}\right)|_{\left(x=1\right)}=- \frac{1}{4}$$$

$$$\int_{1}^{19}\left( \frac{\ln{\left(x \right)}}{x^{3}} \right)dx=\left(\frac{- 2 \ln{\left(x \right)} - 1}{4 x^{2}}\right)|_{\left(x=19\right)}-\left(\frac{- 2 \ln{\left(x \right)} - 1}{4 x^{2}}\right)|_{\left(x=1\right)}=\frac{90}{361} - \frac{\ln{\left(19 \right)}}{722}$$$

Answer: $$$\int_{1}^{19}\left( \frac{\ln{\left(x \right)}}{x^{3}} \right)dx=\frac{90}{361} - \frac{\ln{\left(19 \right)}}{722}\approx 0.245229308893121$$$

Kalkulator Integral Tentu dan Tak Wajar

Hitung integral tentu dan tak wajar langkah demi langkah

Solution