Kalkylator för bestämda och oegentliga integraler

Kalkylatorn försöker beräkna bestämda integraler (dvs. med integrationsgränser), inklusive oegentliga, och visar stegen.

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Solution

Your input: calculate $$$\int_{0}^{1}\left( \frac{\pi x^{5}}{5} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{\pi x^{5}}{5} d x}=\frac{\pi x^{6}}{30}$$$ (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.

$$$\left(\frac{\pi x^{6}}{30}\right)|_{\left(x=1\right)}=\frac{\pi}{30}$$$

$$$\left(\frac{\pi x^{6}}{30}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{1}\left( \frac{\pi x^{5}}{5} \right)dx=\left(\frac{\pi x^{6}}{30}\right)|_{\left(x=1\right)}-\left(\frac{\pi x^{6}}{30}\right)|_{\left(x=0\right)}=\frac{\pi}{30}$$$

Answer: $$$\int_{0}^{1}\left( \frac{\pi x^{5}}{5} \right)dx=\frac{\pi}{30}\approx 0.10471975511966$$$

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Kalkylator för bestämda och oegentliga integraler

Beräkna bestämda och oegentliga integraler steg för steg

Solution