Calcolatore di integrali definiti e impropri

Il calcolatore cercherà di valutare l'integrale definito (cioè con estremi), inclusi quelli impropri, mostrando i passaggi.

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 $$$\int_{-3}^{3}\left( \frac{x^{3}}{18} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{x^{3}}{18} d x}=\frac{x^{4}}{72}$$$ (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.

$$$\left(\frac{x^{4}}{72}\right)|_{\left(x=3\right)}=\frac{9}{8}$$$

$$$\left(\frac{x^{4}}{72}\right)|_{\left(x=-3\right)}=\frac{9}{8}$$$

$$$\int_{-3}^{3}\left( \frac{x^{3}}{18} \right)dx=\left(\frac{x^{4}}{72}\right)|_{\left(x=3\right)}-\left(\frac{x^{4}}{72}\right)|_{\left(x=-3\right)}=0$$$

Answer: $$$\int_{-3}^{3}\left( \frac{x^{3}}{18} \right)dx=0$$$

Please try a new game Rotatly

Calcolatore di integrali definiti e impropri

Calcola integrali definiti e impropri passo dopo passo

Solution