Calculadora de Integrais Definidas e Impróprias
Calcule integrais definidas e impróprias passo a passo
A calculadora tentará calcular a integral definida (isto é, com limites), inclusive no caso impróprio, com os passos mostrados.
Solution
Your input: calculate $$$\int_{0}^{3}\left( \frac{x^{3}}{4} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{\frac{x^{3}}{4} d x}=\frac{x^{4}}{16}$$$ (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.
$$$\left(\frac{x^{4}}{16}\right)|_{\left(x=3\right)}=\frac{81}{16}$$$
$$$\left(\frac{x^{4}}{16}\right)|_{\left(x=0\right)}=0$$$
$$$\int_{0}^{3}\left( \frac{x^{3}}{4} \right)dx=\left(\frac{x^{4}}{16}\right)|_{\left(x=3\right)}-\left(\frac{x^{4}}{16}\right)|_{\left(x=0\right)}=\frac{81}{16}$$$
Answer: $$$\int_{0}^{3}\left( \frac{x^{3}}{4} \right)dx=\frac{81}{16}=5.0625$$$