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Solving integrals/ (4x-x^2)dx

Integral of (4x-x^2)dx dx

The solution

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  1              
  /              
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 |  /       2\   
 |  \4*x - x / dx
 |               
/                
0

$$\int\limits_{0}^{1} \left(- x^{2} + 4 x\right)\, dx$$

Integral(4*x - x^2, (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:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $- \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x\, dx = 4 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $2 x^{2}$
The result is: $- \frac{x^{3}}{3} + 2 x^{2}$
Now simplify:

$\frac{x^{2} \left(6 - x\right)}{3}$
Add the constant of integration:

$\frac{x^{2} \left(6 - x\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(6 - x\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                             3
 | /       2\             2   x 
 | \4*x - x / dx = C + 2*x  - --
 |                            3 
/

$$\int \left(- x^{2} + 4 x\right)\, dx = C - \frac{x^{3}}{3} + 2 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/3

$$\frac{5}{3}$$

5/3

$$\frac{5}{3}$$

5/3

Numerical answer [src]

1.66666666666667

1.66666666666667

The graph

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

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Identical expressions

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Integral of (4x-x^2)dx dx

Limits of integration:

The graph:

Piecewise:

The solution