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 $$$\int_{0}^{2}\left( e^{2 x} \right)dx$$$

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

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

$$$\left(\frac{e^{2 x}}{2}\right)|_{\left(x=0\right)}=\frac{1}{2}$$$

$$$\int_{0}^{2}\left( e^{2 x} \right)dx=\left(\frac{e^{2 x}}{2}\right)|_{\left(x=2\right)}-\left(\frac{e^{2 x}}{2}\right)|_{\left(x=0\right)}=- \frac{1}{2} + \frac{e^{4}}{2}$$$

Answer: $$$\int_{0}^{2}\left( e^{2 x} \right)dx=- \frac{1}{2} + \frac{e^{4}}{2}\approx 26.7990750165721$$$

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Kalkylator för bestämda och oegentliga integraler

Beräkna bestämda och oegentliga integraler steg för steg

Solution