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Calculadora de integrales definidas e impropias
Calcular integrales definidas e impropias paso a paso
La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.
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: $$$\int_{-3}^{3}\left( \frac{x^{3}}{18} \right)dx=0$$$