Calculadora de integrais definidas e impróprias
Calcular integrais definidas e impróprias passo a passo
A calculadora tentará calcular a integral definida (ou seja, com limites), inclusive imprópria, com as etapas mostradas.
Solution
Your input: calculate $$$\int_{0}^{7}\left( \frac{x^{4}}{7} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{\frac{x^{4}}{7} d x}=\frac{x^{5}}{35}$$$ (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.
$$$\left(\frac{x^{5}}{35}\right)|_{\left(x=7\right)}=\frac{2401}{5}$$$
$$$\left(\frac{x^{5}}{35}\right)|_{\left(x=0\right)}=0$$$
$$$\int_{0}^{7}\left( \frac{x^{4}}{7} \right)dx=\left(\frac{x^{5}}{35}\right)|_{\left(x=7\right)}-\left(\frac{x^{5}}{35}\right)|_{\left(x=0\right)}=\frac{2401}{5}$$$
Answer: $$$\int_{0}^{7}\left( \frac{x^{4}}{7} \right)dx=\frac{2401}{5}\approx 480.2$$$