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 $$$\int_{0}^{50}\left( 1250 - 25 x \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\left(1250 - 25 x\right)d x}=\frac{25 x \left(100 - x\right)}{2}$$$ (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.

$$$\left(\frac{25 x \left(100 - x\right)}{2}\right)|_{\left(x=50\right)}=31250$$$

$$$\left(\frac{25 x \left(100 - x\right)}{2}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{50}\left( 1250 - 25 x \right)dx=\left(\frac{25 x \left(100 - x\right)}{2}\right)|_{\left(x=50\right)}-\left(\frac{25 x \left(100 - x\right)}{2}\right)|_{\left(x=0\right)}=31250$$$

Answer: $$$\int_{0}^{50}\left( 1250 - 25 x \right)dx=31250$$$

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Kalkylator för bestämda och oegentliga integraler

Beräkna bestämda och oegentliga integraler steg för steg

Solution