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

First, calculate the corresponding indefinite integral: $$$\int{x d x}=\frac{x^{2}}{2}$$$ (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.

$$$\left(\frac{x^{2}}{2}\right)|_{\left(x=e\right)}=\frac{e^{2}}{2}$$$

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

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

Answer: $$$\int_{1}^{e}\left( x \right)dx=- \frac{1}{2} + \frac{e^{2}}{2}\approx 3.19452804946533$$$

Kalkylator för bestämda och oegentliga integraler

Beräkna bestämda och oegentliga integraler steg för steg

Solution