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Solving integrals/ x-x^4

Integral of x-x^4 dx

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$$\int\limits_{0}^{1} \left(- x^{4} + x\right)\, dx$$

Integral(x - x^4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{4}\right)\, dx = - \int x^{4}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  So, the result is: $- \frac{x^{5}}{5}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
The result is: $- \frac{x^{5}}{5} + \frac{x^{2}}{2}$
Add the constant of integration:

$- \frac{x^{5}}{5} + \frac{x^{2}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{x^{5}}{5} + \frac{x^{2}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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$$\int \left(- x^{4} + x\right)\, dx = C - \frac{x^{5}}{5} + \frac{x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/10

$$\frac{3}{10}$$

3/10

$$\frac{3}{10}$$

3/10

Numerical answer [src]

0.3

0.3

The graph

Use the examples entering the upper and lower limits of integration.