Definite and Improper Integral Calculator
Calculate definite and improper integrals step by step
The calculator will try to evaluate the definite (i.e. with bounds) integral, including improper, with steps shown.
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: $$$\int_{0}^{7}\left( \frac{x^{4}}{7} \right)dx=\frac{2401}{5}\approx 480.2$$$