# 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:** $$$\int_{0}^{7}\left( \frac{x^{4}}{7} \right)dx=\frac{2401}{5}\approx 480.2$$$