Kalkylator för bestämda och oegentliga integraler

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

Enter a function:

Integrate with respect to:

Enter a lower limit:

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

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: calculate $$$\int_{0}^{8}\left( - 2 x^{2} + 16 x \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\left(- 2 x^{2} + 16 x\right)d x}=\frac{2 x^{2} \left(12 - x\right)}{3}$$$ (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.

$$$\left(\frac{2 x^{2} \left(12 - x\right)}{3}\right)|_{\left(x=8\right)}=\frac{512}{3}$$$

$$$\left(\frac{2 x^{2} \left(12 - x\right)}{3}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{8}\left( - 2 x^{2} + 16 x \right)dx=\left(\frac{2 x^{2} \left(12 - x\right)}{3}\right)|_{\left(x=8\right)}-\left(\frac{2 x^{2} \left(12 - x\right)}{3}\right)|_{\left(x=0\right)}=\frac{512}{3}$$$

Answer: $$$\int_{0}^{8}\left( - 2 x^{2} + 16 x \right)dx=\frac{512}{3}\approx 170.666666666667$$$

Please try a new game Rotatly

Kalkylator för bestämda och oegentliga integraler

Beräkna bestämda och oegentliga integraler steg för steg

Solution